oil of snake is the best 😉
Seriously though, the massaging with the oil is more useful than the oil itself – as for actual active ingredients, the menthol/eucalyptus/peppermint type oils act as local irritants and increase blood flow – this may help muscle recovery and the 'deep heat' effect can be relaxing.
As for specifics, the only oil I am aware of that has had any 'proper peer reviewed trials' is calendula (pot marigold).
This has been shown to have anti-inlammatory effects and aid deep tissue healing.
There is less sound evidence that lavender, rosemary and roman chamomile may also be useful.
but TJ24 will no doubt be along soon to put me right……