If you're burning a quart a week, there's a tell-tale sign to look out for; blue smoke coming out of the tailpipe. If the smoke is coming out when you first start the engine and goes away in 15 minutes or less, it's the valve seals. If the smoke is intermittent and random or just constant, it's the piston rings... specifically the oil rings, not necessarily the compression rings. Although a compression test might be a good idea anyway.
If it is the valve seals, it shouldn't be too catastrophic. The valve seals themselves aren't usually very expensive, but the cylinder heads will have to come off and therefore you will need new head gaskets, which also aren't that expensive, but the labor on that might get a bit pricey.
If it's the piston rings, that's a different story... the engine will have to be taken apart completely, you'll need the piston ring set, a full gasket set and while you're in there you definitely want to replace the main bearings and maybe the rod bearings too. It may actually be cheaper to just get a replacement engine if the piston rings turn out to be the problem.
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"Ok, systems check; the battery is discharging, the oil temperature is very high, the oil pressure is very low, the engine temperature is off the end of the scale, I'm running out of petrol... but the clock is correct!"
-James May, in an old, worn out Lamborghini purchased for less than £10,000.
