I don't have the best equipment in the world, and it sounds like the original posters doesn't either, but it gets the job done. Here's how I beef up my sound.
Let's face it, doing a bunch of overdubs on a cassette four track isn't a good idea. All that ping ponging will generate your sound, leading to shitty sounding masters (but you knew that already). When I record a heavy song, I need a thick fatty boomin' sound on the one track. And I get it, but now without some noodling.
1) I only own a Samick LS-31 Fat Strat copy. Killer tone, it doesn't have.
I usually set this to use either, the neck pick-up (deep rich sound), or the top and the middle (deep rich, and versitile sound).
I have some crazy assed economy duncan pick-ups on my guitar, and they sound nice. My body, I believe is made of a composite (english: particle, or plywood), so the sound isn't as rich as a solid wood.
But if you've got
a Fender Deluxe Fat Strat (send it to me), a Les Paul (I agree, nice heavy tone, or any Epiphone made of Korina, you'll get a fuller tone. Korina guitars sound nicer and fuller than any guitar I've ever played in my life.
2) My amp is a Peavey Rage 15 watt. Sure, it's not a tube, but it still sounds surprisingly full for a solid state.
If you've got better, you're damn lucky.
3) Now the secert to my full tone is my DOD TEC4X multi-effects unit.
Adding in just the right amount of DELAY and setting the tone right (I usually go Low cranked, Mid almost nil, and high almost cranked). A kiss of reverb also helps my toneless ass.
4) If you've got the scratch or the bones (money) to fling (buy) a few different sets of strings, do it. Find a set that sounds nice to you. Old strings lack the tone you need.