14g wire on 20amp circuits all over home
Did the &quot;electrician&quot; pull a building permit prior to doing the work you commissioned?  If not, then you have more than one problem here.  If he did, presumably it was inspected and signed-off by the building inspector and perhaps you are misinterpreting what is actually installed.  No professional electrician would install 20A breakers on a 14g circuit.  Doing so is not only dangerous but illegal and unethical.
I suggest you contact this electrician and ask him to explain the work that was done.
If indeed the work was done by an unlicensed person without a permit, you should get a qualified electrician in immediately to inspect and correct the issues.  Yes that might be expensive but a fire is going to be much more expensive.
But to address your root question, NO, this would not cause excess electricity usage.  An electrician should be able to help you find the cause there as well but I'd be looking at the usual high-powered culprits, space heating, water heating, cooking.