Here are some various notes that I can give you about the relevant headphones:
1. I own the Omni, and it isn't going anywhere. I absolutely love it. Headphone taste, as you surely know, is subjective and you will find plenty of people who will disagree as to whether the Omni, LCD-2, or Alpha Prime is the best of the three. There is no obvious choice without listening to them first.
2. The Alpha Prime is a very good sounding headphone. It has that nice planar bass extension. The thing that makes the Alpha Prime different from both the LCD line and the Omni is that the AP have what I guess can best be described as an airier, thinner sounding presentation. That is not to say that the AP sound cold, necessarily, (depends on what you are comparing it to) but they lean away from the rich, full, textured presentation that you will get with the LCD-2 and Omni in favor of more of a clean, detailed presentation. Even though the Alpha Prime uses the same drivers as the Omni you would not guess it at all by listening to them side by side. It's pretty amazing how implementation affects performance.
3. The LCD-2 is a headphone that I used to loathe. I actually used to really dislike all of the Audeze headphones because I felt like vocals sounded compressed, like they were being sung into a tin can. I don't know what changed exactly--I really think it has something to do with how my taste evolved over time, and I gradually began to appreciate how planar drivers sound, but the last time I listened to the LCD-2 it sounded quite good. I thought it sounded like it had a little bit of a mid bass emphasis and vocals were still a bit constrained sounding to me. Overall, though I feel like this headphone is as popular as it is for good reason. I will caution you, however, that there appears to be some really serious issues with drivers failing in the LCD line of headphones and other quality control issues. I've seen myself the wood in a pair of LCD-3s crack for no apparent reason. Also, I've read that current new LCD-2s sound and measure better than older ones--so just a heads up since you mentioned buying them on sale which makes sense in light of this (I'm not talking about Fazor vs pre-Fazor--I guess there was some kind of recent tuning change or something).
4. There are lots of good descriptions of how the Omni sounds out there but I'll give you my brief characterization of it. The Omni has something of a big, rich, and smooth sound. Vocals are intimate and clear and it has precise imaging. Soundstage is surprisingly spacious, and I find one of the best aspects of it is that it has extremely satisfying, speaker-like bass. To sum it it up it has the richest and fullest sound out of the three without being congested sounding.
5. All three of these headphones need amplifiers with power to spare if you are to do them justice. I'm just basing this on your profile page--I seriously doubt the Soundblaster E5 will be adequate for the Alpha Prime or the Omni. I can't say definitely for the LCD-2 but I'd be surprised if the E5 could handle it, either. (I haven't listened to the E5 but looked up some info on it).