As of Generation 7, Pokémon that cannot learn a move from which they receive STAB are:
Magikarp
Ditto
Unown
Wobbuffet (Mirror Coat cannot receive STAB)
Azurill (learns no offensive Fairy-type moves)
Wynaut
Pyukumuku
Silvally: Fairy
Cosmog
Cosmoem
Pokémon that cannot learn a move from which they receive STAB on their own include:
Metapod (Bug Bite is only obtainable through a move tutor or Caterpie)
Kakuna (Bug Bite is only obtainable through a move tutor or Weedle. Poison Sting is exclusively through Weedle)
Togepi (only learns offensive Fairy-type attacks through TMs and breeding)
Smeargle (Has to Sketch)
Gligar (though it learns Acrobatics, it cannot learn any offensive Ground-type attacks through leveling up)
Delibird (though it learns Drill Peck through leveling up, it cannot learn offensive Ice-type attacks without help)
Tyrogue (can only learn offensive Fighting-type attacks through breeding, TMs, and tutors)
Silcoon (identical to Metapod)
Cascoon (identical to Kakuna)
Surskit (learns no offensive Bug-type moves through leveling up)
Ninjask (learns no offensive Flying-type moves through leveling up)
Feebas (learns no offensive Water-type moves through leveling up)
Beldum (learns no offensive Steel- or Psychic-type moves through leveling up)
Budew (learns no offensive Poison-type moves through leveling up)
Gliscor (learns no offensive Ground-type moves through leveling up)
Arceus: Fire, Fighting, Water, Flying, Grass, Poison, Electric, Rock, Ice, Bug, Dragon, Ghost, Dark, Steel, Fairy
Darmanitan-Zen (learns no offensive Psychic-type attacks through leveling up)
Ferroseed (learns no offensive Grass-type attacks through leveling up)
Thundurus (learns no offensive Flying-type attacks through leveling up)
Spewpa (identical to Metapod)
Wimpod (learns no offensive Water-type attacks through leveling up)
Silvally: Water, Grass, Ground, Psychic, Rock, Bug, Dragon, Ghost, Fighting
Minior (learns no offensive Flying-type moves through leveling up)
I believe that is all of them.
