When I went in last month to get my oil changed at the local drive through oil change place, they said my battery terminals were corroded. I didn’t think much of it until I started getting much lower gas mileage. Is this affecting my gas mileage? If so, what should I do to fix the whole problem? Just change the battery? Or get new terminal and battery?
Thanks!
You just need to clean and tighten the battery terminals, I’m sure there are youtubes about it. Or find a good independent shop nearby and pay to have it done.
But I am skeptical that it’s causing your poor mileage, do you notice any other issues while driving?
it’s almost certainly unrelated. if i had to blindly guess: temperatures in your area started getting colder in the last couple of weeks. that would definitely impact your gas mileage.
Many places change gasoline formulations for winter. The winter blend typically gets fewer miles per gallon than the summer mixture. This probably happened around October if you live where it gets cold in the winter.
+1 to both
Additionally, if the OP is one of the people who needlessly warm up their engine for a few minutes before driving in the winter, that will reduce his gas mileage even further.
I agree with all the above advice. If something electrical was causing the fuel not to burn as well as usual, the sensors and computer would detect that, and the Check Engine Light (CEL) on the instrument panel would light up. If it was a severe misfire, it would flash - a warning to shut off the engine to prevent expensive damage.
Well, if you’re interested in some pure BS, maybe the corrosion causes the alternator to work harder to maintain the battery and that translates into more fuel used. 
Seriously, I couldn’t even type that with a straight face. IMHO winter blend fuel is the answer.
Let me guess: The drive through oil change place wanted to charge a nominal fee to clean your battery terminals, right? Don’t fall for it, we’re talking about a DIY job. You can find the proper tools at any auto parts store. If you’re interested in a quickie method of cleaning your battery terminals just pour plain, unflavored carbonated water on them.
Baking soda.
What was your fuel economy before and after? Is your check-engine light on?
Keep in mind that quick-lube places often root around your engine looking for extra work. They could easily knock a vacuum hose or something else loose in the process.