The studs in the manifold that hold the EGR valve are in bad shape and won't hold a nut to tighten down the EGR valve. Any suggestions on how to remove and replace the studs?

 

I'd block off the EGR passages so no debris could possibly enter, spray the bases of the studs with some PB blaster, and hit them with a wire brush from every direction. A good penetrating fluid is key. Do not think WD40 is just as good for this.

Wipe it off, more PB, more wire brushing, until you can see the threads of the stud going into the manifold. Maybe even try heating the manifold with a torch, then an ice cube on the stud to contract the metal, perhaps break the bond.

More PB blaster

Then I'd get a good set of vice grips and clamp them super tight , and very low, and see if you could get a turn out of them. Perhaps file some flats on the studs beforehand. I'd do everything possible beforehand so the studs will not break off in the manifold. The most important of which after the preparation above, is the proper application of torque. Turn the stud without applying a bending force to it.

It's pretty tight in there, you might consider removing the intake after trying the vice grips and a little torque first.

If they break, well then they got to be drilled out and retapped, and I guess the intake manifold needs to be removed so metal filings don't make their way into the cylinders.

Good luck, and I hope Murphy and his law are busy elsewhere during your attempt.