In reverse order: Transcendent blades used to be bugged, It wouldn't scale off of AD correctly (or at least it wouldnt show it. The problem with AP Irelia, is that you're then focusing too much on your "e" spell. Not that its bad, but it's irelia's only AP scale, bar her ult, and her only form of damage. Lets face it - you will never be able to one hit anything. As of late though, they fixed the AD ratio on Blades, making AD the most effective way to build her.

As for Nashors before Omen, I agree. It may still make sense to grab a HoG before the Tooth, if only for some health buffs, but all in all, the CDR/AS from Nashors> health bonus of omen. Infact, as of late I've stopped using Omen all together. I'll be posting my Updated builds in the coming days, Unfortunately, thanks to the timing of this post and the updates to items I havent been able to get a good jungle build together, Though i can tell you it all starts with rushing a Wriggles. Cause its still the BEST early game item ever.

I think if you swapped your build order on your Nashor's Tooth and Randuin's Omen, this build would work better. The offensive benefits outweigh the defensive benefits early game.

Also, Im not sure if I understand you correctly, but Transcendent Blades scale off of AP, not AD. Your build doesn't have much AP, so its not going to hit hard or heal you much. Again, building Nashar's earlier would help this issue a bit.