Court opinions come from the judicial branch. Treasury regulations as well as a slew of other materials come from the IRS, in its role as an administrative function of the executive branch. A hierarchy exists for these primary authorities. After the Constitution, the I.R.C., case law from the Supreme Court, and cases from the taxpayer's own circuit are at the top of the pecking order. Cases from other appellate circuits are only persuasive.
Regulations have different weights depending on the type of regulation.
Yes, the Constitution is the supreme law of the land. However, it is unlikely that you'll be citing to the Constitution in tax research unless you're representing a tax protestor. I.R.C. sections, like any other federal statute, are laws passed by Congress and are applicable nationwide. As with any legal research, pay close attention to applicable and relevant statutes as they will likely be your strongest authority. Tax research rarely depends on just one section of the I.R.C., however, so keep an eye out for related I.R.C. sections or other statutes, in addition to the obvious ones.