I had this problem on a second-hand router a little while ago; I don't know if you'll be so lucky, but in my case there was a nice hole through the side to lock the shaft while removing/tightening the collet nut, the bottom of the bit shank was just near the top of that hole and I could insert an allen key, the rotation of which forced the bit upwards on the corner of the allen key enough to free it.
Which I realise is probably not so useful to you, but this might be: I used oil then, and it made no difference to the future operation of the router with other bits, but it may have helped get the stuck bit out. If a bit of oil between the collet and bit is going to prevent the proper operation of your router, then you're not tightening the collet nut nearly enough. I seem to recall router bits I've bought in the past coming greased to protect them from the elements!
Another thing you might try if all else fails, or if you have the leeway: tap the end of the bit with a hammer, as if it were a nail you were tapping into the router. Often stuck things like this just need to be knocked out of the position they're currently in, and once they're moved - in any direction - they'll move much more freely and could probably be removed by fingers. Obviously if the bit has cutting blades on the end you may want to put a bit of scrap wood over the top and tap that with the hammer instead to avoid damaging the bit.