2013 Fit Base, 5 speed stick. For years, have noticed exhaust oder inside car when I first start it. Naturally, Honda says they don't see anything wrong. I either roll down the windows or close the vent when I first start the car. Oder goes away after a short time. Anyone have any ideas as to what is causing this?

 

It could be an exhaust leak near the engine. When you first start the car the exhaust would build up under the hood and get sucked into the cabin air intake located under the black plastic below the passenger windshield wiper arm. Once you're moving down the road air flow would help clear out the exhaust from under the hood and you might not smell it anymore, but you're probably still sucking some into the cabin. Alternatively, a small crack might leak when the engine is cold and then mostly close up once the exhaust heats up and the metal expands. Regardless of why it's happening, it's not safe to breathe exhaust gases.

Find another mechanic to check your car. Be prepared to leave the car with them overnight so that they can start it cold and see if the smell is evident to them.

 

I don't know if the issue I'm going to mention here applies to you because of your description of exhaust smell vs gas smell in your car. Some Fit owners on this forum have reported a gas smell inside their car shortly before they find out their spark plug(s) are starting to back out of the head or have ejected out of the head on their engine. The spark plug backing out issue is a common problem in Gen 2 Fit engines and a lot of info can be found here doing a search for spark plugs backing out.

 

It's normal for your exhaust to be pretty strong and stinky at start up. That's because that catalytic converters haven't warmed up yet. When the cats get to their operating temperature, the exhaust gets less stinky.

I ain't no expert, by the way. I just hear stuff when I'm out and about.

 

This. My '09 smells for a few seconds on pretty cold starts. Has done since new, despite different plugs/coils throughout its life. It's fine.

 

I have a 2009 GE w/ 180k+ miles.
If your windows are up + fan off, you shouldn't smell it. I do agree that if you are outside of the car upon a cold start, you will smell the exhaust fumes till the cat warms up.

My other car is completely catless, and unless there's an exhaust leak in the engine bay, I do not smell fumes with the windows up + fan off.