There are some things that can make the Omega touchy, like over tightening the stock to barrel and action screws it is even possible to damage the stock and have to reinforce it to get it back right.
Most Omegas are not very touchy, to loose a sabot is an other thing that can cause problems even tumbling.
Most will shoot a wide variety of bullets with 100 gr of BH, if you use crudring [777] you may have to clean well between shots with Blackhorn don't clean until you are finished shooting.
Normally the most accurate load is 100 gr of Blackhorn and a Shock Wave 250 or 50/40 200 gr The hunting load I like best is the 250 Gold Dot or "Deep Curl" which while holding a minute of angle most of the time is not quite as accurate as the SW.
Most of the loads I have tried in mine with a 100 gr of BH and a MMP HPH 24 or a Harvester short black shot under 2 inches a lot under 1.5 inches some under 1 inch.