Just changing the injector loom wont solve the problem as the oil is in the main engine harness if you have oil at the ECU plug.
You can try soaking the oil from the ECU plugs using solvent but this is likely only a temporary fix.
You would need to replace the engine harness which is a bit more expensive. Its relatively easy to do though as everything is plug and play. However if you are not having any problems with misfires etc then change the injector loom, clean up the ECU plugs and sockets, and keep your fingers crossed.
Be careful with the cover gasket and you can reuse it even though they say it should be replaced everytime it is disturbed. They are about £6 so not a disaster if you do break it. Injector loom just unplugs. Make sure the O rings on the main plug are not twisted when you push it through the cam carrier. Dont overtighten the cover bolts. 6 ft/lbs is plenty.
Keep your old loom and soak it for a week or so in some strong solvent such as brake cleaner then hang it up to dry. The best stuff to use if you can get it is MEK (Methyl Ethyl Ketone) which is used in the print trade. Dont use paint thinners because it will dissolve the seals on the injector plugs. Voila one spare harness.