In Game Pokemon Trades

http://serebii.net/heartgoldsoulsilver/trade.shtml
Neat little list of all the in-game trades, but not the point of this thread.

Are natures, level, IVs, EVs, Class*, (and w/e I missed) set by what pokemon you trade, or are they preset/randomized? Or a combination? (random IVs, 0 EVs, same nature and level, or something)

*Class 1 has a different ability as Class 2. If you're trading for something that has two possible abilities, could you manipulate which one you get?

Or in maybe simpler terms: What can you manipulate when receiving pokemon via ingame trades, and what's randomized?

Sent:

L. 78 Adamant Lucario (m)
Ability: Inner Focus
IVs: 31/31/31/15/31/31
EVs: 252 Att / 6 Def / 252 Spe

Received:

L. 78 Brave Steelix (m)
Ability: Sturdy
IVs: 8/30/27-28/17-18/20-21/6
EVs: none

Tried trading the same Bellsprout for the Onix in that one town three times, and each time I got a Hasty Male named Rocky with Sturdy. Going to try a different Bellsprout, since it might go off of stats or something, but I'm not very hopeful. Kind of disappointed, since I really wanted a Rock Head Onix.

Edit: Yep. Still Hasty. Ridiculously unlucky, or its preset. :|