Yes, a compression test would be a good start to deducing why the oil is burning.
For info
Z22SE compression pressures should be between 12 to 15 bar (174 to 218 psi) as long as the following are observed:
Maximum difference between any two cylinders: 1 bar (14.5 psi)
Pressure loss: Not more than 25% max per cylinder
For the 'wet' test add about 5ml of oil to the cylinder. If the readings temporarily improves the compression reading, this indicates bore or piston ring wear is responsible for the pressure loss. If there is no improvement in the reading, this suggests there may be leaking or burnt valves, or a blown head gasket.
Post the results back here and I'm sure someone will be available to help/advise you.
As mentioned above the valve stem seals could also be the culprit for oil burn.
π