Probably the biggest issue with the omega, or certainly the omegas I've owned anyway.
It's a big job and can take weeks to sort out if your working and diy ing the problem yourself even if you know what your doing.
First point do not rush out and buy new tyres. The problem will come back as they wear to the cars settings.
1 rectify any steering or suspension faults. If you have any doubts on any parts or desires to fit new or lower or better or just stock shocks and springs do so at this point.
Check, top shock mount, for play or creaking or cracking, shocks for leaks or bouncyness/loss of damping, springs for breakages on the ends and measure the ride hight in each corner to make sure it's the same within 5 mill all round (wim say 10mill is within limits but in fitting new springs I've found found the ride hight returns to within a couple of mill all round) wishbones, bushes for cracks and splits, steering knuckles for play. Rear donuts are most common failure at the back, but also check the block bushes at the back of the diff to chassis that deal with lateral play and the round cotton real sized bushes dif bushes that deal with play for and aft although these are fairly bullet proof.
Steering your looking at steering idler as main culprit, plus track rod ends and wheel barings, pitman arm and steering box fairly bullet proof although the box may well need adjusting a tickle, be careful though it's easy to bugger it up.
When replacing wishbones be sure to torque the bolts correctly with the wheels loaded to give the correct ride hight when tightening, or they will fail early. Fit lemforder only as the only reliable source, gaybay specials are a gamble if they'll last 3 months avoid first line and buy parts buy in particular for these items. Febi (?) also to be avoided.
2 Once you've done all the work, get it checked for full geometric alignment, tracking alone is a waste of time, the omega can be adjusted for castor angle, camber and toe at the front, and toe which also affects non adjustable camber at the rear.
3 fit new tyres, what's on the car while the settings are all to cock will have worn unevenly and will add to any Ill handling problems or will continue to affect the cars stability until they are replaced, even once set up correctly.
Avoid falcon 912's ESP in low profile sizes, pirelli p zero and avons all get poor reviews on here. Conti sc3 Dunlop, potenza, Toyo proxys and kumho ku 31all seem to get thumbs up depending on your wallet.
Rest assured though, it is entirely possible to get a perfectly good handling omega, my tip, fit lowered sports chassis