When I started playing out of the core set, there was no way two TIEs were gunna beat one X-Wing. Then we started learning how to fly the TIEs and there was no way one X-Wing was going to beat two Ties.
Rebels, like what you have listed anyway, want to plow into the enemy jousting and winning whereas the Imperial ships you have want to get out of arc or stay at R3 as best they can until it's time to come in for the kill.
Are you willing to play ships with whatever upgrades you want despite not having the cards, or are you willing to print off copies of the cards for your matches? I found even with a few ships the right upgrades can really even off the balance for new players still learning to fly, then as you get better at piloting you start to know what you like more. Playing X-Wing and flying your ships is a lot like tone for your guitar rig, it starts in the hands whether it's how you pluck a string or how you set your dial. All the fanciest things can accompany what you do after to help sculpt your attack/tone, but it doesn't mean shit if you can't fly/fret a note
If none of that made any sense, focus on your flying and not your ships for a little bit to find out what's really going wrong in your games.
I assume you're playing 50 point games with those three ships, interested in trying out:
TIE Interceptor w. Saber Squadron Pilot
Outmaneuver, AutothrustersTIE Fighter w. Academy Pilot x2
at all? I've actually gotten into the habit of making pictures of my squadron's pilot and upgrade cards and printing them out or keeping them on-deck with my phone when I'm trying out stuff I don't have the cards for....though at 400+ points for each faction now I'm loathe to find stuff I don't yet have either FFG official or printed off in anticipation of new builds. In huge games I always have the cards on the table, but when it's just a few ships it works out decent to just have a piece of paper that looks like this
or something akin to keep track of your squadron upgrades.