My first guess is intolerance. Most likely dairy, although I am absolutely not an expert. But both my kids have had milk protein intolerance (to different degrees) and whilst Zara stunk for ages cause it took me ages to work it out, Hugh doesn't stink, and he doesn't get any milk products (nor do I since he is BF). He stunk before elimination though.
As for the spit up - that can go either way it can be reflux on its own, or it can be reflux as a symptom of an intolerance.
For Zara, it was a symptom of the intolerance, stopped instantly when put on soy formula. For Hugh, he has reflux as well as intolerance, so is on reflux meds AND elimination diet.