I want to stop EV training my Pokémon for awhile and train them normally so they level up faster. Does this affect my EV points (do all Pokémon give EV values?), or is there an item which stops the Pokémon from getting EV points?
No, there is no way at all to prevent your Pokemon from getting EV if they getting experience (so participating in the fight, and don't die). So you either fight hordes of Pokemon that give the right EV (for example, a stat you already maximised or one that you want to), or complete the EV training.