RE: 25-06 270 30-06
.270 Win for sure out of those 3!
btw, there are many elk hunts reasonably priced, or even just a DIY, you may get luck, if not, you're in the woods for a week chasing them.
And in which cast I think a .270 shooting 130-150grs would be a great deal better on elk than a .25-06 shooting 117grs, course a 30-06 would be even better for elk than a 270, but the 270 would certainly do the job.
For deer, .270 is my gun of choice.