shouldn't effect the air in your home if your furnace is properly vented. Perhaps you have a downdraft problem when the furnace first fires, I'd have it inspected and "tuned up" by a qualified technician and checked for CO (carbon monoxide) leakage ASAP if you suspect this. One really should have their furnace "tuned up", cleaned and inspected if a natural fuel burning system EVERY YEAR (although some say every-other year but if in a northern climate EVERY year) at the beginning of every heating season. Another possibility is that during construction, perhaps your return and feed venting acquired some "yuck"/dust/dirt and again its collecting/condensing on outside walls, running down, and concentrating on the carpets. A properly tuned/vented/adjusted system shouldn't throw that much soot in the air. Now, if you bought the wrong fuel oil, maybe.
1) If you haven't already done so invest in several good CO detectors for your home.
2) have the furnace tuned/cleaned/inspected
3) Replace the air filters on your furnace (you'll usually find them near the intake (from the return ducting system)
4) investigate the expansion joint zones on your home for need of caulking/re-caulking.
5) consider having your ducting system (feed AND return) cleaned by a professional service.
6) clean the carpet areas as previously recommended and observe.
personally I had an experience where before the joists for the second floor were hung, the construction carpenters layed them on their sides and used them to move around, getting muddy footprints on their sides, they then installed them without wiping them down. Same thing for the sub-floor, they never bothered to clean them off, just usually turned them OVER before installing, but in some areas there was black mud on the top. Then the carpet people just installed over the DIRT. Over time, I had the very same wicking situation, I also found that they had failed to properly flash a drip edge at the expansion joint, and had done a sub-standard caulk job, so the "dirt" was 2-fold, actual soil tracked in during construction on the sub-floor wicking up at the "rolled edge of the carpet, AND airborne dirt, etc. blowing/rain driven in from the outside. I spoke from experience there. Ended up having the carpet pulled up, cleaning the floor, backside of the carpet, pad, etc. then having the carpet re-stretched in place and cleaned again. problem solved.
Without MORE info from you as I asked previously, and/or your own investigation, I cannot help you further. "get thee a HVAC inspection, a ladder to inspect your expansion zone for repair, a CO detector, and consider the other things suggested.