your first problem is you are on an old steel bike with no snap and most likely terrible wheels , start with the frame and wheels , you cant expect to hold off trained cyclist on modern tech with an old sloppy steel POS unless you have tremendous athletic ability , i know a guy that can really smash on his steel bike with 33c tires , but he is a cat 1 pro and can output tons of energy .
if you dont want to switch your bike to a more performance based frame and wheel set , just try to upgrade wheels and tires , i dont think your drive train or gear ratios will really hold you back unless you have a triple thats really heavy , or a 2x5 speed thats just not allowing you efficient cadences !
i run sram rival force and red , and notice no difference , BUT i notice a ton of difference between wheels/tires and BB ( bb30 on one bike feels so different compared to 24mm ) oh and you can also try to upgrade your BB to a stiffer lighter one, maybe even convert your BB and crank to a more modern carbon sram ( i find carbon sram cranks for dirt cheap and they always give me a great bang for buck )