Wow, she looks REALLY nice. The good news is, all the important cosmetic bits are intact, like the tank, side panels, stock silencers, airbox and front mudguard. Over here in the UK, those parts are pure unobtainium. About 18 months back a pair of NOS silencers sold for 700 UK pounds.
X7s were
wildly popular over here, even after Yamaha launched the 250LC, because they were several hundred pounds cheaper and not THAT much slower. Also much easier to tune ... which most owners did. Badly. They threw away the airboxes and fitted K&Ns (causing repeated seizures). They fitted Micron chambers and junked the stock silencers, or crashed a lot ... which is why you can't get stock exhausts or airboxes.
The good news is, they are such a simple motor to work on and spares are plentiful. If she starts well from cold the crank seals are probably OK. The smoking is likely to be one of two things:
1. Oil pump setting. Suzuki dramatically simplified the oiling system on the X7 and its little brother, the 200cc X5. Unlike previous GTs which had separate oil feeds from the pump to the crank bearings AND to the cylinder, the X7 just had one feed to the inlet tract for each cylinder. This mimics the Yamaha / Kawasaki approach. The pump is behind the gearbox sprocket cover and owners rarely adjusted it, so it's probably set on the rich side.
2. Exhausts clogged with crud. X7s were
VERY prone to this, and it kills their performance in no time while making them smoke like a chimney. The good news is, the exhausts are two-piece making them easy to remove. Pull them off, remove the baffles, then poke a stick up the exhausts, give them a caustic soda enema, beat them with a rubber mallet, etc to dislodge all the crap. The problem is in the exhaust itself, not the baffles which usually just get oily.
I would suggest checking the oil pump setting first, then take her for a spin. If she's healthy, she should run sweetly up to 5,000rpm, then feel a bit edgy and unsettled for 500rpm, then above that the exhaust note gets a hard edge and the bike should GO. If it doesn't do that, clean the silencers
