Being that Pokemon Trainer and Diddy are two of my favorite characters, I feel that I can answer this.
Squirtle: It's not very good for Diddy that Squirtle can jump over the bananas easily. However, because of the bananas, Diddy has a major range advantage. Off stage, they both gimp each other rather easily, though Squirtle is a little better at it. Diddy's air game KOs better than Squirtle's, and Diddy's recovery is better. I say that the matchup is in Diddy's favor.
Ivysaur: Ivysaur has the range advantage, yes, and Ivysaur has the advantage on his ground game, yes. However, he also does have decent lag if he misses an attack, and the bananas outrange Ivysaur's attacks. Ivysaur is very suspectible to being overcome by bananas and being edgehogged. This matchup is in Diddy's favor.
Charizard: Charizard edgeguards and KOs Diddy very easily. He's also in the air more, meaning that he's less suspectible to Diddy's bananas. However, when he's on the ground, Diddy easily destroys Charizard due to his large size. Once again, the bananas are perfect for linking into one another and punishing Charizard's lag. It's in Diddy's favor.
Overall...
Diddy > Squirtle
Diddy >> Charizard
Diddy >>> Ivysaur