How big is your grass team and did you fail by timing out or by fainting? Eggy is supreme and helps with both of course, but if you timed out a level 30 Vileplume or Victreebel has sufficient DPS.
As stated already, neutral damage is not viable and Machamp and Raikou are pretty much the only non-grass options you should consider. At L30 they are a bit too slow but can round up the team if you don't have 6 good grass mons.
Stick to grasses, and preferably with SoB. A Victreebel with LB won't hurt you too much, but seed bomb is a bit weak in terms of DPS. It will still do better than Machamp, though.
The first time I tried Omastar, it took me three attempts. I failed first with three Exeggutors, a Venusaur, a Machamp, and a Raikou, and it wasn't all that close.
The second time, I subbed in a Victreebel for the Raikou, and it was closer, but I still failed.
The third time, I subbed in another Victreebel for the Machamp, and I won with 20 seconds remaining (I also subbed in a RL/SoB Vileplume for the RL/SoB Venusaur, but I don't think that mattered, and if anything, the Venusaur is probably better). I didn't dodge at all against rock blast, and the mons were all between level 30 - 33. You'd think I'd have better survivability with the Machamp in there, but that was not the case, because the grasses do so much more damage.
The key is doing a lot of grass (SoB) damage, plain and simple. Don't try to overthink it and use non-grass mons, unless you don't have six big grasses, but then it is going to be tougher. BS/SoB Eggs are the best by far. Eggs with C/SoB or ES/SoB aren't nearly as good. If you have at least three of them at level 30+, and other big SoB grasses (with grass quick moves) to fill out the lineup, you should be good to go. Try not dodging at all, especially against rock blast. Dodging just wastes time and DPS.
That's a way stronger team than the one I used, except for the psychic quick moves on your Eggs. ZH and ES definitely hold back the Eggs against Omastar, both in terms of type effectiveness, and energy gain.
Do you have another Victreebel, Venusaur, or decent Vileplume you can sub in for the ZH/SoB? Level 30 is good enough. Then, put the ES/SoB Egg in the last slot, or better yet, sub in another double grass attacker for that one too.
Here's a picture of my winning team. The Exeggutors all have BS/SoB, the Vileplume and second Victreebel have RL/SoB, and the first Victreebel has RL/LB.
If you put in the Venusaur and the SoB Vileplume in place of the ES & ZH Eggs, I don't see how you can fail. If you can power them (or the SoB Victreebel) up a little, so much the better, but you should have enough firepower as is. With the compromised Eggies out of there, you can put the LB Victreebel in the last slot to smooth out the damage output.
For those wondering how much difference it really makes having BS on Exeggutor, I ran Pokebattler simulations with my level 35, CP 2670, 14/14/12 Exeggutor, using all the different quick moves.
The times to win against Omastar with "unknown moveset" and no dodging are as follows:
BS/SoB: 142.9 seconds
C/SoB: 166.9 seconds
ES/SoB: 163.4 seconds
ZH/SoB: 175.6 seconds
Obviously, it's a big difference, and note that confusion is actually a little worse than ES in this case.