You don't need a bigger filter: you're already filtering perfectly, that's the problem.
Filters turn Ammonia (very bad) into Nitrite (quite bad)
They also turn Nitrite (quite bad) into Nitrate (not so bad, but not great at high concentrations)
Your filter is working ideally, turning all the toxic ammonia into less toxic nitrate (via nitrite): it just happens to be that you're fairly heavily stocked and have messy fish, so your Oscar is making lots of ammonia which is being converted to nitrate.
Basically there are only three ways to remove/reduce nitrate from your tank (or four, kinda)
1) Water changes to physically remove it. Very simply, removing 50% of the water removes 50% of the nitrates. As such, it is impossible to get rid of with water changes alone. It sounds (assuming your kit doesn't max out at 160ppm) like you're getting a solid 160 and halving it to 80 once per week, before it bounces back to 160 ovver the course of a week: so your fish are producing about 80 per week. As such, you're only ever going to vary between 80 and 160ppm. If you did 50% water changes twice per week you could reduce it to between 40 and 80ppm (removing 40ppm twice per week instead of 80ppm once a week). This involves twice as much work but keeps your nitrate level at half of the current level.
2) Reduce the bioload - you're heavily stocked in terms of bioload so removing some fish or downsizing the Oscar or plec would help. I removed my common plec as he was a heavy load producer. Admittedly I couldn't get rid of my Oscar, I like him too much
but perhaps you've got another fish you're less attached to? Reducing feeding works, too - there's nothing wrong with a slightly hungry fish and Oscar's can be fed every 2 or 3 days easily. Mine gets fed anywhere between 2 and 5 times per week, but I aim for 3 or 4 alternating weekly. They'll beg for food, but that's because as far as I can tell it's impossible for an Oscar to not want food: he'll be fine without it some days though.
3) Plants absorb the nitrate and turn it into plant matter, making them grow. By removing some of the plants (ie cutting them back) you remove nitrate from the tank. This is basically the same effect as a water change but the plant keeps nitrate down in the water, and you have to do it less often. Your problem here is that your Oscar will most likely eat the plants and excrete them as ammonia again...
4) Similar to plants, but artificially done with special medias available from most filter manufacturers. These absorb the nitrate and you simply remove them when they're full.
In reality the cycle is basically
Fish eat Nitrogen in the form of plant matter
Fish excrete ammonia
Ammonia is converted to nitrate and nitrite - all three of which are absorbed by plants (although mostly nitrate)
Fish eat the plants.
Ad infinitum
The ideal alternative would possibly be to add a sump to your tank (or move to a sumped tank), then you can have plants and algea in a refugium away from the hungry fish. This is probably the direction I'll be heading once I upgrade. Otherwise it's a case of water changes and possibly nitrate-absorbing media.