Thank you everybody for your input! Here is an update: It is a fabric issue, not a Mod Podge issue. The FQ that gave off the fumes was from Walmart (Waverley collection) not Connecting Threads as I had originally thought.
How do I know? I applied mod podge to a FQ from Connecting threads, allowed it to dry and ironed it....absolutely no odor or fumes whatsoever. I tried another FQ from Walmart and guess what? Fumes and odors. I tried another FQ from Connecting Threads and just as before, no fumes or odor. So two FQ's from Walmart with fumes/odors, and two from Connecting Threads with zero odor. I can only assume that WM uses some chemicals on their FQ's that reacts unfavorably with the Mod Podge.
Aside from the fume/odor issue, I found the Mod Podge worked excellent for raw edge applique, with NO FRAYING. I definitely will be using this technique again but only on prewashed fabric or fabric that I know will not react with the Mod Podge.