I dunno if it's worth mentioning this, but I had a couple of instances, when I was in my late teens and early 20s, where I owned a couple of vehicles and this happened.
NOT straight after an oil changes though - that may be just one of those weird coincidence things?
Anyway, heaps of white smoke on start-up, which smelled nauseating. It would go away while driving under acceleration, but down hills with my foot off the gas, back it came, and at idle.
Turned out it was a pinhole in the brake booster diaphragm, and at high vacuum, the engine was hauling brake fluid in through the intake manifold and burning it. Unbelievable smell.
Second time it happened, on a different car, that was the first place I looked, and it was actually making a faint "whistling" sound.
Last up, and only slightly related, (no smoke), my next door neighbour was having seemingly incurable idling problems on a 5.0 litre Holden V8. It would stall at the lights and if he drove VERY slowly, it would die.
Full throttle pretty good, but a bit hairy around town at a steady low speed.
He fitted a new carb kit, then a complete new Holley, glugs, leads, distributor cap and rotor, drained and replaced the fuel, then did the PCV, (not necessarily in that order...).
Still ran like before.
Guess what?
Yup, booster diaphragm was split -it had gone all dried out and hardened.
Diagnosed by pulling the vacuum hose of it, and blocking it with my thumb. idled just fine, thanks. Reconnect to the boster, nope. Ran like a bag pf rocks.
So, a rebuilt booster, and it now runs like a Swiss watch.
The super-stinky smoke on my own cars it what gave it away, and it was thick, white smoke, not blue and smelling like burning oil.
Maybe???
Seems weird about the heater going out at the same time, unless a vacuum leak in the booster somehow affects it's operation? There are vacuum hoses all over the place on some vehicle heaters...