Is there any reason to NOT use my ammo mods? How can I use them to greatest effect?

For the most part, nope. No reason not to always have an Ammo power activated.

An exception might be if you are specced into, for example, the final rank of Incendiary Ammo and the explosive effect would be inconvenient for some reason (Perhaps you're trying to snipe a target without blowing up a strategically placed explosive barrel or something.) Those situations should be pretty incredibly rare though.

Ammo Powers will never leave you vulnerable, they will not cost you credits, will not damage your weapons, and will not kill your fish. They will allow you to do more damage, apply useful debuffs, and, with upgrades, carry more rounds.