Congress and the Fifth Amendment
Congress can't literally "force" you to testify with torture or something.
You would refuse to testify on the ground of the 5th Amendment.
Congress, that is full of lawyers, 30% of House members and 51% of Senators are lawyers, and has many lawyers among the 31,000 staff employees in Congress, understands the 5th Amendment, as applied to Congress, perfectly well. And, you can bring your own lawyer with you to your scheduled time to testify (and in communications with the Congressional committee issuing the subpoena in advance of that time) to educate Congress if it seems ill-informed.
You don't have to say much as a threshold manner to invoke the 5th Amendment right not to testify (although Fifth Amendment objections to some really basic questions like "what is your name", or questions you have no personal connection to like "what is the org chart of the DOD", aren't going to work). The burden is on Congress to show that you can't invoke the 5th Amendment because you don't face a risk of criminal liability.
Congress can also circumvent your 5th Amendment rights by granting you what is called "use immunity" for you testimony, which means that it can't be used against you in a criminal prosecution (other than for lying to Congress or refusing to testify). One way that it can do that, if the criminal law that is a concern is a federal one, is to have the Justice Department agree to provide use immunity for the testimony. If the Justice Department doesn't provide immunity voluntarily, or a risk of state criminal liability is involved, Congress can also ask a judge on the U.S. District Court for the District of Columbia to provide you with use immunity for your testimony from all state and federal crimes as authorized by 18 USC §§ 6001-6005 as noted in the answer from alexg.
Also, corporations do not have a 5th Amendment privilege under U.S. Constitutional law, so the 5th Amendment is not a valid objection to a Congressional subpoena of corporate records (although sometimes some other evidentiary privilege like the attorney-client privilege or doctor-patient confidentiality could be claimed as a defense to producing those records).
Congress would bring a lawsuit in the U.S. District Court for the District of Columbia to hold you in contempt of Congress for refusing to testify. You would present your 5th Amendment defense to the judge. The judge would rule on the question. If you or Congress disagreed with the ruling, the decision could be appealed to the U.S. Court of Appeals for the D.C. Circuit, and conceivably, from there, to the U.S. Supreme Court. This process has produced a modest body of case law, some of which is cited in the answer from alexg.
There have been eleven contempt of Congress prosecutions since 2019. The process is a familiar one to the members of Congress and judges involved in handling it.
Various Forms Of Liability For Congress Related Misconduct
§ 1983 does not apply to Congress
Is it just as simple as pursuing a 42 U.S. Code § 1983 - Civil action
for deprivation of rights lawsuit or is there some other type of
justice you could pursue?
No.
42 U.S.C. § 1983 applies only to state and local governments and officials (and the D.C. local government and its officials) and only imposes civil liability. It provides in the pertinent part that:
Every person who, under color of any statute, ordinance, regulation,
custom, or usage, of any State or Territory or the District of
Columbia . . .
Bivens actions provide only limited relief
The federal government analog to a § 1983 lawsuit is called a Bivens action (and arises under federal common law. But, the rights its protects are narrower than those protected by § 1983 actions (only a few select rights like the 4th Amendment are protected) and it only applies to executive branch-like activity. It doesn't apply to quasi-legislative or quasi-judicial activity in the executive branch, or to legislative activity in Congress including most Congressional investigations. But Bivens would apply, for example, to misconduct by law enforcement officers employed by Congress in an organization chart way, when they are engaged in law enforcement activities (e.g., if they make an unlawful arrest), even though they are not part of the legislative rather than the executive branch of the federal government.
For example, if the Capitol Police water boarded you during a Congressional committee meeting to get you to testify there (which would violate rights covered by Bivens), you would have a Bivens action claim against the Capitol Police officers who were involved in doing so, although not against the members of Congress involved in presiding over that hearing and asking them to do so.
The Capitol Police officers who were involved would also have criminal liability in this situation under federal law, although I couldn't cite chapter and verse to cite to the exact federal criminal statutes involved without more research.
Members of Congress and Congress itself have legislative immunity
Would there be any redress aimed at the speaker or other members of
the house that forced you to testify against yourself?
No.
Members of Congress and the institution itself, have basically absolute immunity from civil liability, subject to a few exceptions where it has expressly waived that immunity by statute, mostly in the area of employment laws for Congressional staffers. The United States government itself, of which Congress is a part, also can't be held criminally liable.
Members of Congress also have immunity from almost all civil and criminal liability for most official acts under the Speech and Debate Clause of the U.S. Constitution. This is found at Article I, Section 6 of the U.S. Constitution and says:
They 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 returning from
the same; and for any Speech or Debate in either House, they shall not
be questioned in any other Place.
Each house of Congress can discipline its own members
Members of Congress who engage is misconduct in the course of their duties can be disciplined, but only by the House as a whole, in the case of representatives in the U.S. House, and in the case of the Senate as a whole, in the case of U.S. Senators, in proceedings that the legislative body initiates, in accordance with the rules of those respective houses of Congress in a proceeding that is quasi-judicial but has a strong legislative/political component to it. This authority flows from Article I, Section 5, Clause 2 of the United States Constitution which states:
Each House may determine the Rules of its Proceedings, punish its
Members for disorderly Behaviour, and, with the Concurrence of two
thirds, expel a Member.
For example, one of the members of Congress from Colorado, Lauren Boebert, was heavily fined for repeatedly and flagrantly violating U.S. House of Representatives rules including those related to not submitting to metal detector screening when entering the House floor and related to not wearing masks during COVID.
