The Speech and Debate Clause of the Constitution protects senators' and representatives' right to freedom of speech when debating in Congress, separately from the First Amendment freedom of speech available to everyone. The Supreme Court has ruled that there are certain limitations to First Amendment freedom of speech. Is this also true of Speech and Debate Clause freedom of speech? Is there anything that is illegal to say in Congress?
The speech or debate clause is about immunity, not freedom of speech.
The speech or debate clause protects members of congress not only from criminal prosecution based on covered speech but even from having to testify about their speech in a trial about something else, and also from being interrogated about it by investigators.
This immunity serves the separation of powers. For example, it prevents the president from using the threat of investigation to put pressure on members of congress to vote a certain way. Indeed, it protects members of congress from such influence coming from anyone, because it also applies to civil suits, in contrast to the first amendment.
Much of the litigation concerning the speech or debate clause has not actually concerned speech but instead actions and documents. An aide to senator Mike Gravel was protected from testifying before a grand jury about his involvement in the acquisition of a copy of the Pentagon Papers. After an FBI search representative William J. Jefferson's office, the FBI was ordered to return privileged legislative documents seized in the search -- but not other documents.
But this question focuses on actual speech in congress. I was not able to find any cases with casual research tools available on the internet where this was at issue. Wikipedia mentions a defamation case, Wuterich v. Murtha, but that seems to have been dismissed on the basis of the Westfall act rather than of the speech or debate clause. Perhaps someone with access to better tools will be able to find something, but for now, as far as I can see, the answer to your question
Is there anything that is illegal to say in Congress?
They can’t commit treason, a felony, or breach of the peace
The Senators and Representatives shall in all Cases, except Treason, Felony, and Breach of the Peace, be privileged from Arrest during their attendance at the Session of their Respective Houses, and in going to and from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.
The Courts have found that this privilege extends to all of a Congressperson’s speech while acting as a legislator and also extends to acts of their aides while acting under direction. The full limits of “acting as a legislator” have not been tested but it’s likely to be very broad and include everything that is not clearly and uniquely personal.
Treason requires an act, not just speech. There are some felonies that can be committed by speech alone, for example, conspiracy or incitement. Breach of the peace will be defined in local law but those cannot be Constitutionally vague and must pass strict scrutiny - speech alone is almost certainly not a breach of the peace.
Now, a Congressperson can be held to account by the rules of their house and any censure, up to and including removal, is not justiciable - that is, it is not subject to judicial oversight.