I think you've got it backwards. The point of the washers is to take up space inside the frame so it doesn't need to be bent in order to tighten on the wheel.
First - A quick release axle should NOT stick out past the outside edge of the drop out (where the axle sits in the frame). The axle should extend a little bit (.25-1.0 cm) past the end of the outermost locknut on the axle on each side. But that extension should not be long enough to go all the way through the drop out and stick out past the outer edge of the frame. If it is, that might be part of why you can't tighten this down.
Ideally, you would take off the outer lock nut on each side of the axle and add the washers under them. Doing this usually means readjusting the bearings on the axle though and you might need cone wrenches you don't have.
Short term, you can just put the washers on the end of the axle. This isn't great, but is probably OK to test out if it will work. It's OK to use up some of the extension of the axle as long as a tiny bit still sticks out the end. Just enough to catch on the frame. But it is really the QR skewer than holds the wheel on.
All this said, if you have to use a large amount of force to clamp the QR skewer down even with the washers, I don't think you should use this wheel. Either you're going to mess up the frame or the skewer's going to break or something else that could cause damage or a crash. If so, measure the frame between the dropouts in the back (inside dimension) and go back and try to get a wheel that will fit.
Also, just to make sure...You know that the quick release does not work like a wing nut, right? You don't just spin it until it tightens down. A very common mistake. See here:
http://bikeride.com/remove-install-wheels/