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For the eyeliner, wipe your eyes with a towel to remove excess oil. If you're trying to apply it to your waterline then idk, but you're not really meant to do that anyway as it can clog up ducts which then requires clearing by a doctor
The other problem you might have with oily eyes is creasing, basically as your open eyelid folds up, the eyeliner can collect in the creases.
I clean my eyes and use a very light moisturiser first, then towel to remove any excess. That usually saves most of it, but a little finishing powder or even just a neutral eye shadow will help prevent it too