Yes, the ev count stays unless you reduce it via the EV-reducing berries. (Also not stat gains aren't always going to come straightaway on the next level up unless you're a high level (in which there's only a decent chance of that), but they all get turns into stat boosts when you hit 100 (or do an online battle temporarily).
[*]HP
[*]Hoot-hoot (1pt)[*]Location: Basically everywhere, and quite common. A few areas, Route 1-6.
[*]ATTACK
[*]Bellsprout & Ekans (1pt)[*]Location: Route below Violet City
[*]DEFENSE
[*]Geodude, Onix, Rhyhorn (1pt)[*]Location: Rock Tunnel, Dark Cave, Union Cave
[*]SPECIAL DEFENSE[*]Metapod and Kakuna (2pts)[*]Location: Ilex Forest
[*]SPECIAL ATTACK
[*]Ghastly (1pt)[*]Location: Sprout Tower
[*]SPECIAL DEFENSE
[*]Tentacool (1pt)[*]Tentacruel (2pts)[*]Location: West of Cherrygrove City - Surf on water
[*]SPEED
[*]Magikarp (1pt)[*]Location: Fish in any body of water using the Old Rod