A solid opening repertoire definitely helps, but you're talking as if that's the only way to improve.
IMO the 5 basic areas are:
Openings, strategy, tactics, endgame, and annotated game collection.
My usual advice for improvement is to pick your weakest area and study it. For the vast majority of players their weakest area is not openings.
I think your openings are fine except the old benoni. Don't play that, you're just giving yourself headaches, especially if you don't know a lot of theory. You'll get better positions playing a queen's gambit declined knowing next to nothing than you will a benoni knowing next to nothing.
Since you're 1600, I'd say you're pretty darn good at not blundering material to simple tactics. IMO usually the next step is strategy and endgames. I recommend Pachman's Modern Chess Strategy or Soltis' Pawn Structure Chess. For Endgames I very much like Dvoretsky's Endgame Manual. Yes even for 1600 because that's when I read it, but I understand others will disagree with me, and even recommend Kmoch's Pawn Power in Chess instead of Soltis. Their recommendations are fine too. This is just my two cents. Read book reviews and choose for yourself.
I've been 1600 rating for a long time and I'm sick of it. I want to cross the 1800 barrier but I've shown zero signs of improvement over the past 5 years and it's really disheartening.
As white, my openings are: king's gambit (against e5), grand prix attack (against sicilian), exchange variation (against caro-kann) and advance variation (against French).
As black, my openings are: caro-kann defence (against e4) and old benoni (against d4).
Despite playing the same openings for years, I still haven't mastered them. I still don't know all the lines. I've been lazy and haven't bothered to learn them properly. So that leaves me with 2 options if I want to improve:
1) Learn the lines properly. Master these openings.
2) Abandon these openings altogether and learn something more solid.
Which approach should I go with?