Very few people have reported being able to stop taking omeprazole (or any other PPI) suddenly without experiencing severe acid rebound. Your body responds to the years of producing no stomach acid like it has to make up for all the lost time. For most it's necessary to gradually reduce the dose over period of 2-3 weeks, or maybe longer, to prevent this.
If you are taking two per day, switch to one. Or if you are taking one and you can't find a lower dose OTC version to start your withdrawal, if it's pills, try cutting them in half. If capsules, try opening them and dumping half out. You can buy empty gel caps at most pharmacies to save the other half.
If you have a bad reaction from halving the dose, then go back up and start again by taking out 25% instead of half. If half works, do that for a week or 2 and then try it every other day. You can also try the different dosages of H2 blockers over the counter (Zantac) during your withdrawal. They block acid in a different way, but they block less than omeprazole, so they may be useful at some point in your gradual cut down on the dose.
Take it slow, and add more back if you get any sudden heartburn. It works differently for everybody, so you'll have to feel you way through this.