An exhaust smell in our house but no CO poisoning symptoms.?

You are too stupid.

Get a carbon monoxide detector!

View the flame in the burner when it first starts up. Then in a minute or so the blower motor will come on. At the moment the blower comes on, observe the burner flames and see if they move at all, like a small breeze is blowing on them. If so, chances are you have a cracked heat exchanger. Try to view the burners through a sight glass instead of removing a panel if possible, so the flames don't get effected by the open panel.

Be careful though, the biggest scam in the industry is telling you that you have a bad heat exchanger and need a new furnace.

Yes, could be very possible

Do not wait for symptoms of CO poisoning. The symptoms are loss of consciousness and death. Also Co does not smell, so you need a detector. 

The smell in the house might be a gas leak, which is dangerous because it can explode. On the other hand you might have a lot of dust in there that is burning and creating a smell.

I would consider a new furnace, or at least get it serviced. The service guy will tell you why it smells. 

CO is odorless, so the smell is something else.

One thing that came to mind is a small natural gas leak around the gas valve ...when the furnace is off….then, upon start up, you get a quick blast of that ….Whatever the smell is you should get it checked out ASAP ...as there should be no smells coming from there …other than the occasional mouse that may have died in the duct work…...yuck!

CO itself is odorless…. but with a gas furnace it’s a really good idea to have a detector or 2……HD sells the digital CO detector in a 2pac for 30.00.

FFS buy a CO detector! Guesswork is dangerous.