Let's assume it's one of my Luigi avatars. All Luigi would have to do to defeat Toad is throw him into a pit or other hazard. However, Toad is holding a Gamepad that allows him to manipulate the world around him Super Mario Maker-style. It's close, because Luigi has great platforming skills, but Toad can move the platforms at will. I'm gonna say that Luigi will win, but just barely.
Hrmmm... it all really depends on which version of Tingle we're talking about here, the Tingles present throughout most of the mainline Zelda games aren't particularly fighters in any capacity so Luigi is more likely to beat them in a fight. The Tingle present in Rosy Rupeeland is a smidgen tougher in comparison but he still had to rely on bodyguards to help him with skirmishes for most of the game save for a small handful of boss fights like Captain Stalfos, Dora Dora and of course the big showdown with Uncle Rupee with his multiple forms so he might stand more of a chance against Luigi but probably not by much.