You mention "batteries", as in more than one. Do you have 2 twelve volt batteries in parallel, or 2 six volt batteries in series?
Batteries left discharged can develop sulfation as well as a shorted cell. If it's shorted cell, the remaining cells will be charged like crazy and can get hot, smoke, stink real bad (hydrogen sulfide, aka sewer gas). The other possibility is that the inverter has gone bad and is way overcharging the batteries. You need a voltmeter to know for certain - if it's above 14v then the inverter is probably bad. Most likely, it's the batteries and the inverter is OK. If the inverter is bad, you probably need new batteries as well.