I work for a utility, and if you call in and ask they will tell you the average use for a property. It's the same calculations they'd use for a budget bill. So if the house was occupied over the last year or two, you can see if it was also costing the previous occupent that much. That will help you determine if it's a larger problem, like lack of insulation, or something specific to your usage patterns.
I second what someone else said about estimated billing. This is a common reason for high bills. If for some reason the utility can't get to your meter, including something their fault, like a meter reader shortage!, they'll estimate. How many months in a row they can do this depends on the laws in your state. You could definitely call and ask if your bill was estimated.
The old fridge will make a significant difference, sometimes up to $100 a month or so, but that certainly doesn't account for all the extra you're seeing.
Also second what someone said about energy vampires. Some really common ones are chargers, along with TVs and other things that maintain indicator lights of clocks. Some TVs don't really go to sleep even when you turn them off, just keep running at reduced power so they're warmed up whenever you're ready to turn it back on!
When it comes to measuring particular appliances, an energy monitor is deifnitely the way to determine precisely where problem appliances lie. Sometimes a utility will have them to borrow, and local libraries sometimes do too. Definitely worth checking before buying one.
Also check to see if your utility offers free energy audits. Many do, and sometimes they even provide free supplies, like weatherizing kits, CFLs, etc.
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