In the current gens your Pokemon's EV's can effect their stats even without leveling, for instance by feeding your level 100 Shiftry a carbos it will still gain 2 or maybe 3 in speed. There will be no announcement for this boost however. Now lets take the same shiftry and make it 10 years younger, back in gen 3 and such that shiftry would've NEVER gotten that carbos because of it's level, which was 100, so it could never level up to collect the boost
You're likely playing an older game if your EVs are only popping in only when you level up (+7 in attack and other unreasonably high raises) and the reason your Pokemon seem to be gaining no evs at higher levels is because they probably hit their EV limit, and can no longer even obtain EVs.
It would be nice to know what game you're talking about and how you're raising your Pokemon so we can give a better answer