What groin injuries can massage therapy help with?

If it is a strain. If the groin injury is a muscle strain, massage can be helpful. However, groin injuries should be evaluated by a doctor to rule out other causes, like hernias. The most common strain involves the adductor muscles, but any ligament or muscle strain in the groin/hip area can be treated with massage.
See below. I assume that you are referring to muscular injuries. The groin area involves a large number of muscles and determining which one(s) are injured is important to focus therapy. Massage to any muscle can help after the initial inflammatory period. A physical therapist and orthopedist could help you determine what course you need.