Very few, in my experience. I flew the F-18 for 2,500 hours and a lot of time in Inuvik, as well, and during that 2,500 hours, I never lost a single engine. Both continued to operate all the time. I never hit a bird in an F-18 during that time, either.
The other point I would add, anecdotally, is that fighter aircraft don't spend a lot of time in the environment where birds operate. They're normally up very high. The takeoff and landing phases are the critical phases, obviously.
Fortunately, at the airports we operate at, there are very effective bird control measures to minimize the number of birds. Hence, our number of bird strikes, in my personal experience, are very low in the F-18.