Theres usually no problems mixing enamels and oils. The problem lays more with the thinner.
Indeed both can be mixed to shorten oils drying time, or extend enamels drying time. Both together are great for dry-brushing.
Most thinners will work for thinning out the mixture for painting .... but be careful .. some are so strong that they damge/lift the already dried coat.
For washes, the thinner can cause even more problems. At worst, it could lift your already dried paint or its just un-suitable for washes. What tends to happen is the pigment particles seperate, and instead of a nice, even, wash colour, you get little clumps of pigment and then areas of no paint at all.
I have tried several thinners; white spirit, balsamic terpentine, etc. but none work consistently like Humbrols own enamel thinner.
I have used a particular brand of white spirit with great success for thinning and washes, and then on the next model it lifted the paint. Now I stick with humbrol as I dont want to risk losing work already completed. Even if you only use it for washes, a little bottle goes a long way. For the few pennies saved by using something else, its not worth the hassle.