Do MIM Strats have a veneer and if so, does it affect the tone? Which Fender guitars have veneers?

Some do, most don't. Only the Mexican Standard sunbursts I think. The way to tell is to look at the belly cut out on the back of a strat. It will be a solid colour. Because the veneer can't cover that area.
I'm pretty sure the translucent colour finished Mexican Deluxe guitars don't get such treatment.

No it doesn't affect the sound of the guitar in the slightest.

_________________
No no and no

Yep, exactly what nikininja said. Only veneer these days are the sunburst MIM Standards to cover up the 4 or more mismatched pieces of alder. I would just like to add that there was a period in the 90's where even sunburst American Standards got the veneer treatment. They sounded fine to me. It's just a cosmetic thing.

_________________
Obligatory gear list: Fender, Rickenbacker, Gibson, Gretsch, Vox, Martin, and more Fender.

makes sense, thanks for the info.

I believe that this was during the period where poplar was substitued for alder.