All that affects is how much travel the levers have before the brakes engage. If you can lock up the brakes before the lever hits the handlebar, you're not lacking braking power, even if the caliper is opened up a little bit.

(personally, I set up my brakes a little "loose", because I feel like I get better modulation and not such a sudden on-off response like I get if they're really close to the rim... that's mostly a personal preference, though)

Replacing cables won't make any difference unless they're about to snap or if they have a LOT of drag. The biggest problem of dirty, dragging cables, though, isn't in activating the brakes, but releasing them. Your hands are stronger than the return spring on any brake, and if anything gets affected first, it's the brake spring opening back up and pulling the cable taut after you've released the lever. If that's not an issue, then the cables don't need replacing.

Again, the next logical step for the biggest improvement on your bike is new rims. $100 wheels on a $5 bike is still a whole bike for around a hundred bucks, and it's probably still better than any $100 department store bike.