My dwarf is in a strange mood. How can I fix him?

Minor Spoilers!

If the dwarf has a strange mood he has probably taken a workshop which if you query will list the objects or hints to objects which he needs to fulfill his mood. If he fulfills his mood good things will happen. If not, some form of FUN will ensue.

You can try to execute him, with magma, spikes, or some other devious trap. You cannot order another dwarf to kill him though.

IF the dwarf goes stark raving mad, you may kill him as if he was an enemy.

Avoiding spoilers, have you considered what he likes doing for a craft? Does he have the ability (workshop, raw materials) to do that?