If you have been running the car for sometime with a very low oil level, you could've damaged the engine by now - you did say that your oil pressure light has been flickering for quite a while - so that means the car hasn't been getting lubricated properly for quite a while.

Assuming what you say that there's no leak, how does a K20A burn through 4litres of oil every 5000km? Sounds like the engine wasn't very healthy to begin with. The weight of oil shouldn't have any impact to the way the engine runs as you have described.

Is there smoke coming out your exhaust when you drive? I'd get a compression test done on the car...