Thanks for the quick reply,
While I cannot diagnose your dog's problem via the internet I can tell you the following :
Omeprazole is in fact sometimes prescribed for dogs at a dose rate of 0.5 mg per pound of their bodyweight once a day so it is not poisonous to them per se. On this basis the top dose for your dog would be 6 mg.
Clearly then the 20 mg is an overdose, this drug is said to have a wide margin of safety in dogs but clearly you have to act.
1. If your dog swallowed the tablet within the last hour you should immediately induce vomiting and recover the drug that way. For the sake of speed I will give you a link on how to do this best : LINK
2. If you fail to induce vomiting or see any odd symptoms you should contact an ER vet without delay. Such symptoms may include nausea, vomiting, flatulence, diarrhea, urinary tract problems or nervous symptoms.
If I have not covered your question fully enough or you would like to ask more I will be online for the next hour or so and I will be at your disposal.Scott Nimmo BVMS MRCVS