Re:
It shouldn't feel squirly and weird.
If it does then the setup is wrong.
Weird is fine though and more than likely its the bars. Mine always feel odd on the straighter bars compared to my swept back a few degrees ones. All mine are flat bars.
Tyres was the one thing that killed a bike. Some of the round profile contis like the speed kings just didn't feel right.
Ride it a bit till bars and things are not noticed, should happen in a normal 20 mile ride.
Or your forks are setup too soft of course.
Could be a bike is too small as they do feel odd then especially if your not used to riding smaller bikes.
Looking at the picture it looks like you could ride the next size up. It's a drop to the bars and a long stem for a 94 bike. Might just be that and they're not off road tyres.