I just purchased a 2001 GSR with 103K on the clock. I had! a similar problem with the car. Previous owner took really good care of the car. Using 5w-30 Mobil 1 every 3000 miles. I only later found out I was loosing 1 qt per 1000 miles. I also have an 94 Integra that burns ZERO oil in its 7500 OCI with the s2000 filter.
I fixed the problem with 4 simple steps. (copied from my Team-integra.net post) If you own an Integra and are not a member, you are missing out!
I just bought a 01 GS-R. And my first tank netted me 22 MPG. I pretty much was [censored] off, as my LS was getting 33 mostly highway.
I noticed black soot on the rear of the car, would come back after washing, so figured it was my exhaust and was running rich.
I changed 4 things to fix the soot problem, Oil consumption, and in turn, fixed the MPG problem.
1. Extremely clogged Fuel filter. Replaced with new OEM. The fuel that leaked out was so filled with particles I was astonished. I ran a Fuel system cleaner (seafoam) for a tank after the fuel filter change. And through the IM.
2. Replaced the PCV Valve. Oil consumption dropped to zero. Don't think this would affect MPG issue
3. Pulled the spark plugs, checked the gap. was at .044 (way to go one6motorsports!). My manual calls for .052 gap. Regapped and reinstalled. (iridium NGK plugs)
4. Replaced the original Primary O2 sensor.
My last fill up I am at around 28.5 MPG with winter gas. And every fill up I am seeing a marked improvement. ( I think its the pennzoil synthetic cleaning things.)
I managed to improve the gas millage and fixed the oil consumption.
Hope some of this helps, I love the integra, and wish a similar car was made now.