The Radziwiłł family cannot be considered equal in any way with mediatised houses of the Holy Roman Empire. Although the first member of this family achieved the title and dignity of a Reichsfurst in 1547 (Mikołaj "the Red" Radziwiłł) and they were one of the richest and most powerful families of the Polish-Lithuanian Commonwealth and Europe as well, they were not descended from and never was a rulling house. They held extensive landholdings, mostly in Lithuania, which they ruled as almost sovereign lords and had their own large courts and even held some military power under their own command. They used some of their land possessions' names, such as Ołyka, as parts of their titles, claiming they were Dukes of Ołyka. But their lands were formally not even fiefs and they were subjects, not vassals of Polish kings (who were also Grand Dukes of Lithuania). In fact, their major holdings, including the estate in which Ołyka was the central and eponymus part, held the status similiar to a fee tail (they were held by members of the family in fideicommis). The fee tail was hereditary in primogeniture and could not be divided, sold or mortgaged. The other grandest Polish families also held fideicommises (in Polish known as ordynacja).
I know only one case of a member of the Radziwiłł family who became owner of an estate of the Holy Roman Empire and thus, achieved a higher formal status outisde Poland. It was Prince Janusz Radziwiłł (1579-1620), head of the Clavinist branch of the family, who in 1618 bought the Lordship (Herrschaft) of Lichtenberg in Bavaria for 160 000 guldens. From 1616 he lived in exile in Germany and the purchase of the land, preluded by a close involvement in local political life in alliance with the Protestant princes of the Empire, was a move to achieve the said status and become a rightful member of the estates of the Empire. His goal was to weaken the position of the Emperor as he wished that a possible war between the Emperor's coalition and the Protestant estates of the Empire, which he planned to financially support, would finally give him the desired status in a reward. What could be more interesting here in this thread, in 1613 he married Elisabeth Sophia of Brandenburg, daughter of the Elector John George. It was the first marriage of a Radziwiłł with a member of the House of Hohenzollern in history. In 1620, after seven years of marriage, Janusz Radziwiłł died and the Lichtenberg passed under control of his widow, who in 1628 married secondly Duke Julius Henry of Saxe-Lauenburg (and had one son, Francis Hermann, with him).
Janusz and Elisabeth Sophia's son, Bogusław Radziwiłł, who for some time in his youth lived at his mother court in Lichtenberg, married his cousin Anna Maria Radziwiłł, who was a wealthy heiress of her line of the family. They had one daughter, Ludwika Karolina, who eventually became the heiress and last member of the entire Protestant branch of the House of Radziwiłł. I don't know if Janusz Radziwiłł has finally achieved his goal and was considered by members of the HRE as equal but his son, Bogusław, continued this struggle to assume a sovereign power in his own way, by signing in 1656 a treaty with the rulers of Sweden, Brandenburg and Transylvania as part of their alliance againt Poland in the Second Northern War. The signatories divided Poland and Lithuania between themselves, the invaders, with Bogusław Radziwiłł achieving the territory of the entire Nowogródek voivodship as his sovereign realm. There are also no sources stating that Janusz's son, Boguslaw, ruled (or even owned? because as far as I know, Elisabeth Sophia held the estate) Lichtenberg after his father as it seems that he tried to gain even more than his father did in his own way. Moreover, he was not involved in the internal German politics like his father was and he dedicated his entire life and all efforts to strengthen his position in the Polish-Lithuanian Commonwealth and eventually to establish more and more independent rule in his Lithuanian lands.
Ludwika Karolina Radziwiłł, daughter and heiress of Bogusław Radziwiłł, was the second member of her family married into the House of Hohenzollern. She was extremely rich, having owned over 1,000 villages and a couple of cities. Her first husband was Louis of Brandeburg, son of the Elector Frederick William, whom she married in 1681. However, Louis died 6 years later. Widowed Ludwika Karolina married then in 1688 even grander than the first time, with her second husband becoming Charles III Philip, the Elector Palatine. Thus, Princess Ludwika Karolina Radziwill became the Kurfurstin von der Pfalz. She had three daughters and one stillborn son with him, while only the youngest daughter named Elisabeth Augusta Sophie had produced issue which continued the line of Janusz and Bogusław Radziwiłłs in female-line. The Kings of Bavaria were among her descendants. The Ludwika Karolina's vast estates in Poland and Lithuania were a subject of a long-time and high-profiled dispute between her Catholic paternal relatives from an another branch of the Radziwiłł family, other magnates of the Polish-Lithuanian Commonwealth and her German ancestors. The noble estates of Poland claimed that the so-called Neuburg domain, which was Luidwika Karolina's inheritance, cannot passed to the Wittelsbachs because by marrying the Elector Palatine in secret from the Polish government, she broke the prenuptial agreement of her and Prince Jakub Ludwik Sobieski, son of King John III Sobieski. Finally, the Radziwiłł lands passed to their agnatic heirs, the Radziwiłłs of Nieśwież who became even more richer after that. It was this branch of the family which produced the third Radziwiłł who married into the House of Hohenzollern many years after the disputes over Bogusław Radziwiłł's estate. In 1796, Prince Antoni Radziwiłł, the hereditary ordynat of Ołyka and Nieśwież, married Princess Luise of Prussia, niece of the late King Frederick the Great. Although he was one of the most powerful Poles, this marriage was not considered dynastic as he was not of equal birth with Princess Louise. Even more extensive research and consultations on the Radziwiłłs' status and heritage were held at the Prussian court and between genealogists in case of Antoni and Louise's second daughter, Eliza, who was the love and desired bride of her maternal cousin Prince William of Prussia, who later became King William of Prussia and finally the first German Emperor. Although the Prince's father, King Frederick William III personally accepted his son's choice and wanted him to marry his love and a close family member at the same time, there were some powerful movements at the court that did not wish a Polish noble lady by birth to marry the heir to one of the most powerful European royal houses. That included the relatives of William's late mother, Louise of Mecklenburg. Despite Frederick William III's efforts, including a request to the Tsar of Russia for adopting Eliza and thus, elevating her status, the Hohenzollerns were finally forced to reject the possible marriage between Prince Williama and Princess Eliza. In 1826 William married Augusta of Saxe-Weimar. Eliza Radziwiłł was for some time engaged to be married with Prince Friedrich of Schwarzenberg, but it failed to. What's interesting, the House of Schwarzenberg was a mediatised house and thus held equal status with the House of Hohenzollern. However, it was very much lower in rank, wealth and power than the Prussian rulling house so a Radziwiłł princess was good enough for them.
Continuing in the 20th century, certain members of the Radziwiłł family intermarried with European royal houses. In 1909, Prince Hieronim Radziwiłł, of a very different branch of the family than Prince Antoni and Princess Luiza, married Archduchess Renata of Austria, from the Teschen branch of the House of Habsburg-Lorraine, who was a first cousin of Alfonso XIII of Spain. The marriage was considered morganatic at the Austrian court. The couple's eldest son, Dominik Radziwiłł married in 1938 Princess Eugenie of Greece and Denmark, granddaughter of George I of Greece. I dont know if the marriage was considered dynastic, but I think it was, considering for example Prince Christopher's first wife, who was an American and a double divorcee but was accepted as Princess and an HRH.
To sum up, status of the Radziwills was never that of sovereign or equal with sovereign. They were sometimes accepted as marriage candidates for members of Europe's royal and princely houses but sometimes were considered unequal with them. An another powerful Polish-Lithuanian noble family, the Czartoryskis, were on the other hand descended in male-line from the rulling Grand Dukes of Lithuania from the House of Giediminas. However, IMO they were mediatised to Poland ages ago and lived as ordinary Polish noblemen for too long to be considered equal with the mediatised houses of the HRE. A Czartoryski prince married a sister of Archduchess Renata, Princess Hieronim Radziwiłł, but that marriage was also considered morganatic. The father and great-grandfather of Prince Adam Karol Czartoryski y Borbon, current head of the family, were married to Bourbon princesses but in France there was never such thing like morganatic marriage, and the Spanish Bourbons have much lower grooms accepted for their princesses in record, for example Count Andrzej Przemysław Zamoyski, who married in 1885 Princess Maria Carolina of Bourbon-Two Sicilies. Their daughters, Countess Maria Karolina Zamoyska married in 1923 her first cousin Prince Rainieri, Duke of Castro.