Yoshi's double jump armor does very little against Squirtle's combos. Landing B-Air -> F-Tilt -> Jab is a true combo at low percents (get rid of the F-Tilt at middling percents). U-Air has enough range to avoid a mid-air jump -> N-Air when Yoshi is getting juggled. D-Air gets Yoshi out of his mid-air jump quickly and does not allow him to N-Air out of it, much less anything else. Yoshi is also heavy enough for combos to keep working until mid-to-high percents.
Squirtle can chase Yoshi's airdodges and either B-Air/F-Air/U-Air before an attack/airdodge or land another aerial after the first one whiffs to tack on extra damage after an airdodge. Water Gun messes with Yoshi's B-Reverse and Egg Toss stuff.
Ivysaur can land Bullet Seed if Yoshi tries to get tricky with his pokes. The predictable movement of Yoshi's mid-air jump allows for a mix-up between Up-B or an aerial chase. Razor Leaf keeps Yoshi's Egg Toss and shielding in check. N-Air is safe to do against Yoshi because he can't do normal stuff out of shield. Ivysaur does generally well with edgeguarding Yoshi and he's one of the easiest characters to land a U-Smash on, from what I can tell.
Charizard's Flamethrower can stop Egg Toss in most situations, and he can create great shield pressure against Yoshi. B-Air helps him in the air, and U-Air allows Charizard to juggle Yoshi pretty well. Both Flamethrower and Rock Smash work well against a variety of Yoshi's moves.
In general, I think Squirtle probably does the best, but not by much. Ivysaur is a close second, and Charizard is decidedly the worst, though it's not a terrible matchup. I haven't played enough Yoshi to tell for sure, but I would say that Yoshi has an ever-so-slight edge in the matchup.