Will my new Nikon Lenses work with an old film SLR?

No harm will come to any of the lenses or the camera—I have an FE2

You’ll have three issues to deal with:
1. If the lenses don’t have an aperture ring, you will not be able to adjust the aperture on the lens, and it’ll be stuck at the smallest aperture (probably f/22). The FE doesn’t have any way to set the aperture in camera (not even a Program mode).
2. If the lenses are true DX crop lenses, you won’t get full coverage on the film. That is, the image will not fill the frame, and you’ll likely get a circular edge to the image. (Maybe not a problem, but something to know about). You’ll be able to see this in the viewfinder, so it’ll be obvious the first time you play with it. My Tokina 12–24 is full frame to 18mm, so I’ve generally not had to worry about this.
3. The manual focus on that era of lenses is “stiff”, and some good Nikon and other current lenses have relatively stiff manual focus. So when focussing, it’ll be easy to knock the focus off. Not a huge deal, but something to know about.

Thanks heaps!

I’m curious as to what what would happen seeing that they are gelded thus you have no control over aperture with an older film camera that was made back in the day, AFAIK you’ll have no control over it except it being wide open, but as stated above remember you will indeed not get full coverage on the film so in the end it won’t be 100% worth it, would be interesting to see the results though.

Well my 70–300mm has a manual aperture ring so that should be fine, the 18–55mm kit lens doesn’t but that’s alright. I’m buying a film SLR for photography at school so I’ll tell you how it goes.

@joeysefika, your kit lens is dx, it won’t cover the frame. Also, shooting at f/22 not only will lead to long exposer times (requiring a tripod) but will also result in a low resolution image. Above f/11 diffraction becomes an issue. Diffraction is bad, makes images less sharp.