Burning smell in a 2009 impreza?

Question edited for clarity.
Question moved to model category.

Try cleaning the Throttle Body and MAF (mass air flow sensor). If that doesn't fix it, an auto electrician with a pro grade scan tool computer can diagnose which sensor is causing it to dump fuel in 'Short Term Fuel Trim'.

Videos for both jobs below.

You need to get this checked by a good mechanic SOON. Burning smell could be something simple or something Dangerous! Could you describe the smell? How strong is it? A 'Burnt Plastic' smell could be a serious one as this could be a wiring 'short' which if not sorted could cause an engine fire. **HOWEVER** Check the obvious stuff first!
Sometimes when you have topped up the engine oil any small spills can heat up with the engine and cause a smell. Usually a 'musty' burnt cooking oil smell
A sweet smell could be coolant. You can get this if a radiator hose or the radiator is leaking. You sometimes get this smell if the head gasket has 'blown'.

Check the blower motor resistor and the wiring harness to the blower motor. Common GM issues.

take it back and tell them

vechicle could be burning oil.or look under hood for valve cover gasket leaks. oil leaking on hot engine and exhaust manifold will cause burn smell.check drive belt could be slipping.make sure brakes not dragging or if you replace brakes pads you will smell burn smell until new brake shoes or pads break in.

White smoke is usually a sign of the engine burning coolant.
You may have a gasket leak where the coolant is leaking into the cylinders when the engine is off, and you are burning it out until it warms up.

check to make sure you dont have anything (plastic bag, etc) burned and stuck on the exhaust, othere than that it could be a normal smell associted with the different materials getting hot, i would compare it to another like vehicle and see, could also be trapped odors in the heater core caused by a previous smoker or bacteria growing, gm sells an odor elimnator that works pretty well

Burnt smell after starting 2013 Chevrolet Equinox. Turned key starter turned over slowly then started drove car however strong electrical burning smell after starting pulled over seen smoke coming from under vehicle. Car wouldn't start even with a jump starter just clicking sound then nothing while horrible smell of burnt electrical from under the hood. Towed it home it just clicked once. Lights, horn, flashers dash and power locks all working fine never had any problems. Thoughts starter or ??

I think you could use this manual method instead.. My nephew
use it to repair my car and it's totally perfectly fine now. Here's the website he bought it from. www.reliable-store.com

probably leaking rocker cover gasket ,oil slowly lands on exhaust,ive got one and had exactly the same symptoms and rocker cover gaskets were the issue