Yes you need an inverter to get 120 volts alternating current from a 12 volt direct current battery
cant hurt but you should do some math. I think you will find not only is there no free lunch, when it comes to this plan, there is no cheap lunch either.
80 watt panel means maybe 5 (or so) amps charging at best. Optimistically figure ten hours of good sun, thats 50 amp-hours (give or take). Cloudy days mean less, maybe none.
uses maybe 120 watts, thats 1 amp at 120 AC and 10 amps at 12 volts. Optimistically figure 85% efficiency for the inverter, you need almost 12 amps of 12 VDC to use the fridge
with an inverter. Running fridge
for 24 hours is 282 amp hours.. a bit more than the 50 you got from the solar
if you were lucky. Outlets.. that depends on what you want to use them for. Many things (like cell phone chargers) have 12 volt DC options and that works better with a 12 volt battery
than using an inverter to go one way then the cell phone charger to go back to low voltage. Lights
are normally 12 volt anyway, and LEDs will sip power.
And we have not even mentioned the battery (or batteries) needed.
I'm not saying that you cant use an inverter, only that you should do some through planning and run some calculations before spending money.