I don't have the ODAC, although heard good things about it. I only have the O2 amp and for the price its quite excellent, so if that is reflective at all of the ODAC then you should be fine. I have two headphones that are awesome all rounder: HE-500 (HE-400 should also be good) and Denon AH-D2000.
Since your budget is $400, HE-400 is $400 (unless you get it used - great value here at head-fi forums) and you're left with nothing for DAC and I don't know how it will pair with HE-400.
If you get a D2000 used, you can get ODAC and the ALO should be able to power the D2000. D2000 are very efficient headphones. Both HE-400 and D2000 have awesome bass and are great all rounders. The HE-400 is faster however.
With your budget, the D2000 + DAC would work out better. Although when both D2000 and HE-500 are amped properly with good source, the HE-400 will be better than D2000, my HE-500 is in another league to my D2000. Although that's not to say that D2000 are bad, in fact, they are (or used to be, since the price bump) one of the best at their price range. I still enjoy my D2000 very much - very comfortable.