Actually, there are a couple of strategies. If you want a water/solvent- or soap-free alternative, judicious roughing of the surface of the panel with fine sandpaper or wet-or-dry abrasive paper should work. Do that outside or wear a mask. Long ago, when everyone painted houses and walls with oil-based paint, those paints came with the instruction to dull the previous surface with sandpaper.
For less work (and less sanding dust), go with a liquid cleanser.
Look for a brand that explicitly says 'cuts grease.' If if also says, 'requires no rinsing,' then that's even better. NOTE: you do still want to rinse, at the very least with a more-than-damp cloth.
'Cuts grease' and 'no rinsing' points to an ether-alcohol surfactant (fancy word for 'soap'). Your water-soluble oils very likely include an ether-alcohol surfactant to make them friendly with water. Once that solvent evaporates, you have traditional oil paint... which is why it's sometimes hard to add water to oil-soluble paints that have been left on the palette during a long session.
In the US, Formula 409 does well. I have a gallon of cleanser from home improvement big-box Home Depot labeled Zep Formula 505 that also works, though you have to use a very light hand with that one. Hmm, "Formula 505" - wonder if they knew about Formula 409 when they named this one? Wear gloves.
The EU has restrictions on ether-alcohols (AKA glycol ethers) in household chemicals, so I wouldn't know what to suggest for those outside the US.
If you want some chemical fun, read the Wikipedia article on 2-Butoxyethanol, which is in Formula 505 and used to be in Formula 409, but may or may not still be there. Green groups don't much like it, but I'm not sure I've ever read what they DO recommend.
Don't over-wash with the cleanser or you'll cut too deeply into the oil priming.