Effexor can definitely cause diarrhea which usually subsides in a couple of weeks. If it lasts longer then that be sure to contact your physician.
I was on effexor for three months and it did give me loose bowel movements for about two weeks. I have IBS, but this was much worse. It did go away, so if you can take the discomfort for a bit longer it might be worth it all. I wish you all the best, let us know how it works out okay?