As of Generation IX, there are no Pokémon that learn all entry hazard moves. This is because only Gigantamax Copperajah can set Sharp steel down with G-Max Steelsurge, and it cannot learn any other hazard moves but Stealth Rock.
Excluding G-Max Steelsurge, Smeargle is the only Pokémon that learns Spikes, Toxic Spikes, Stealth Rock, and Sticky Web. It generally chooses to run Sticky Web with Ceaseless Edge and/or Stone Axe, rather than most of the status moves themselves. Thanks to having basically every move available, Smeargle's versatile moveset makes it both a valuable Sticky Web setter and suicide lead.
When this question was first released, the only hazard moves were Spikes, Toxic Spikes, and Stealth Rock. These are the Pokémon that learn all three:
/nds toxic spikes, stealth rock, spikes:
Clodsire, Forretress, Gligar, Glimmet, Glimmora, Gliscor, Mew, Omanyte, Omastar, Pineco, Quagsire, Smeargle, Wooper-Paldea
Of these Pokemon, Glimmora, Clodsire, Gliscor, and Mew are the best hazard setters.