Figure a worm drive Skil draws let's say...12 amps. At 120v AC.
So shift the decimal point and it's now 120 amps at 12v DC.
120 amps X 12v = 1440 watts.
So a 1500w inverter would handle it...except it probably won't because the Skil has a huge momentary startup load. Pretty much any other power tool that will plug in to a normal 15a 120v wall outlet will be less than that - except for a chop saw or a welder.
Now as to the battery...
Well, if you have a 120 amp*hour battery, then figure you'll get maybe an hour out of it before it's totally completely flat. Of course, running a battery completely flat shortens its life a LOT, so you probably won't want to do that.
Standard bar type fridge will draw a lot - usually around 11 amps or so...so figure an hour run-time until dead battery. Good 12v DC fridges like ARB, Engel and Novacool are hella more efficient.
Bottom line: Big inverters need big battery banks (anything over 400w is big - a 400w inverter draws up to 34a from a 12v DC supply). Or they need the truck engine running (at high idle speed) while you use them. You'd be better off with a small generator.
Current: 76 E-250, bubble-top, self-contained|couple of old Yamaha enduros
Previous wheelers: 41 Willys|78 FJ40|78 Bronco|84 Bronco|74 Ramcharger|78 Ramcharger|79 D150 PowerWagon|77 D100|79 D400 dually, converted to 4WD, utility bed, 10' Lance|75 Westy|69 Scout, RHD|bunch of others|bunch of bikes|couple of boats|couple of motorhomes|blah blah|so what|not my idea|just doin' what I'm told|wank wank|this space for rent|candy is dandy|but liquor is quicker