So with EVs, one Pokemon can have only up to 510 EVs in all of its stats, and only 255 EVs in one stat. When you're EV training, you usually train up to 252 EVs in a stat, because only every 4 EVs take effect (255 being indivisible by 4). Also, the term usually used is not "my Pokemon has high EVs", but "my Pokemon's EVs are all used up", since there's a 510 cap.
As for checking EVs - you can't. You can call Bianca on the Xtransceiver if you're in Black & White 2, and there are various other NPCs throughout the different generations who will tell you vaguely what your Pokemon's EVs are, but they won't tell you for sure.
The best way to keep track is to do it yourself and record what you battle. This is really only done if you're into competitive battling. EV training is also usually done post-game, because if you're still playing through the game, you will have to battle trainers and their Pokemon will give EVs that you might not want for your Pokemon.
It's safe to say that your Misdreavus' EVs will be all over the place, and won't add significant bonuses to her stats. Additionally, in-game wise there's actually not that much of a need to EV train unless you're using the Pokemon for things like PWT or Battle Subway. Versus gym leaders and even the Elite 4, as long as your level is a few above theirs, your EV spread won't matter that much.
If you want to properly train your Misdreavus' EVs, you'll need to reset her EVs via Berries.
List of Pokemon by EV Yield
^ This list will show you which Pokemon to fight for what kind of EVs. Defeating different Pokemon will give different EV points.
Since you battled randomly with your Misdreavus, her EVs will have been randomly gained.
Marriland - How to EV Train
^ This guide is really useful. It takes you through EV training, and though that's not what you asked for, it'll clear up a lot of things about EVs.
IVs = Individual Values
IVs effect your Pokemon's performance, and are set from the moment you encounter your Pokemon, whether through the wild or through hatching.
Each stat has an IV, so HP, Atk, Def, Sp. Atk, Sp. Def and Speed all have a number. The highest IV a stat can be is 31, lowest being 0, so the 'perfect' Pokemon has 31 IVs in all of its stats.
IVs will determine how 'superior', lets say, your Pokemon stats are for its species. Obviously even a Pachrisu with 31 IVs in all of its stats will still struggle against a Zekrom with 0 in all of its stats.
Before Gen III, IVs used to affect shininess of a Pokemon, but now it's determined by your Trainer ID instead.
Bulbapedia - IVs - Iinked before, but Bulbapedia explains the basics of IVs.