IMO, you should install the inlay before you stain or oil the stock.
I say this because although the water based, alcohol based or acid stains won't change the inlay cavity size after the wood has dried, any of the oils you use will cause the wood to swell which will make the inlays cavity smaller.
If the inlay is in place, the wood will grip the inlay tighter closing any small gaps that might exist.
If the inlay is not in place when you oil the stock you will end up having to recut the pockets edges to get the inlay in place.
As for expoxy, if you use this method roughen the back side of the inlay and clean it with acetone before applying the stuff. The rougher the better.
Also, I should point out that using this method to hold the inlay in place is counting on the bond between the wood and the epoxy only.
Wood, expands and contracts as the moisture in the air changes and over time this can break the bond between the wood fibers and the epoxy.
It is best if you use some mechanical fastener to hold the inlay in place.
Although some folks make their own tiny nails I've found that drilling a 1/16 inch hole (or smaller if you can find a drill bit) thru the inlay and then installing a straight pin works well.
I cut the pin off leaving only about 1/8-3/16 inch of its shank below the head to serve as the "nail" and then file the head flush with the surface of the inlay.
Well, once, I didn't file it flush. That was on a fish inlay and I put the pin where the fishes eye would be and left it stand proud. :grin:
