How big should battery be to power two strips of led for few hours?
Buy an LED strip and a cheap multimeter.  Then power the strip with the battery and measure the current with the meter.  Take the current and multiply by the time you want to use it for, in hours.  So if it draws 0.5 A and you want it to last 2 hours, then you multiply 0.5 amps times 2 hours to get 1 amp-hour.  Batteries are rated in amp-hours, so connect enough of them in series to get the voltage you need, and then connect enough in parallel to get the capacity you need (battery amp hour does not change in series, but they add in parallel: two 1 Ah batteries in series form a 1 Ah battery at twice the voltage, two 1 Ah batteries in parallel form a 2 Ah battery at the same voltage).  I don't think a pair of AA batteries will get you the run time you want, though.