You could upgrade your brakes, but before you decide to do that for an old Huffy, you may want to consider getting new wheels with alloy rims. You could probably get some used 27" wheels off of Craigslist or ebay for $50 or less. Alloy rims will help you stop much better.

You should, at the least, get your wheels trued. If they're not true, then this would be a reason why the front's squeeking so much. (Think that would cost you about $20 for both wheels at the LBS, maybe less--my LBS prices are NYC prices.) ANY LBS will do that.

While you're at it, you might want to just get the bike tuned up, too. If this bike is in the shape that I'm beginning to imagine, you may just need to replace the brake cables and/or housings, and have the levers/brakes adjusted. The brake pads can be replaced by something different, but if you have new pads on them already, they should at least work better than the old.

In general, unless something violent has happened to the brakes (e.g. collision), there shouldn't be any irreversible reason why they don't work as they did before, other than a lack of maintenance on the bike. There is nothing inherently ineffective about a sidepull brake.

If you want better, more specific help, find out the actual brake brand (look on the brakes themselves) and also the lever brand. Posting a pic or two wouldn't hurt, either.
Good luck.