As a TO, Prof and LL who started in VGC, I'd say the kind of thing you're looking for is really comprehensive and not something that is easily summed up on a spreadsheet.
For illegal EV's, you'd have to check everything in depth via some sort of IV calculator-type deal. But even then, you'd have to tease apart specialized EV spreads. This would be incredibly time-consuming to check a full team, and would likely not be useful even if you were to only hack-check people who have made Top Cut or something similar, since hack-checking everyone this way would take many computers/people/minutes (potentially hours). Alternatively, with the use of an outside party/device *cough* Action Replay *cough* you could load a code that allows you to view the EV's and IV's of a pokemon easily.
As for Illegal balls, that's a whole other problem. An example would be that if a Pokemon knows a breeding-move only, it could only come in a Poke Ball, but that requires you to look at what moves are possible, then affirm that the ball is legal for each and every Pokemon. Obvious hacks (Cherish Balls, etc...) can be easily spotted, but the rest requires an on-the-spot knowledge.
As for move combinations, you could try using something like Pokemon Online or some other online teambuilder and just building a person's team/moveset, and if it comes up with an error, then you know you've found something. Again, a fair amount of time would go into this, but if it were for a top 8 or top 16 with at least 2-4 computers, you could reasonably move-check everyone in a matter of minutes. This also could check for abilities provided you have a built-in filter on.
That said, all of these processes would be done separately, and the whole process would take a very long time :| But if you're committed, then that's probably the best way to make it work.
For IV's/EV's, I really see an outside device/software as the only way to hack-check. Combine this with a battle simulator like Pokemon Online and you could check a team pretty thoroughly. I don't know if PO will check for impossible IV spreads though (ex: There is no legal way to obtain a Latias with 31/0/31/31/31/31 as the PID does not exist). If you had enough computers and volunteers, you could probably hack check everyone about as quickly as a deck-check might go... of course this requires as many computers available as you would have people for deck-checking.
Hope that's helpful if nothing more.