Do stomach muscle strains come in waves? more intense for no reason at random times?

Yes.: I am assuming that you are referring to the outer abdominal muscles and not intra-abdominal pains of the intestines. Abdominal muscles are trunk muscles that are active all the time to stabilize your upper body against the effects of gravity and therefore a muscle strain can be aggravated from normal daily activities.

Possible : Muscle strain can be worse with movements. Movement can cause pain and pain can result in spasm which leads to further pain . This can present as pain in waves . Depending on which muscles we are talking there can other reasons too like if it's abdomen then it could be abdominal cramps rather than muscle strain .