240v outlet not delivering 240 volts
Well, first of all...you probably didn't have an actual 277volts.  What you had is a cheap meter.  I have seen all kinds of whacky voltage readings from the $5 harbor freight meters I have laying around.  

The only place one sees something other than 120 or 240 volts in a "normal" residential setting is the very rare "3 phase power".  The vast majority of homes do not have any 3 phase power available.  It has to be run to the house specifically as an unusual setup.  When this exists in a home it would add "208V" to the list of possible voltages.  Again, very rare and probably not at your house.

The only place you would see a real 277V is in a big factory. It is normally used for HUGE machines such as big welders and bigger shop equipment than you have probably seen before.  Normal DIY shop equipment runs on 120V.  Big shop equipment runs on 240V.  HUGE shop equipment requires 3 phase connection with the 208V "wye 3 phase" mentioned above.  It is extremely rare in a house.  The 277V delta 3 phase would never be seen in a house, and only rarely in any commercial building you have been in.  It is typical only in large factories.

Now as for what's probably wrong...you probably have a loose connection or a broken wire on one side of your 220 connection.  This would give you 0v between the two hots, but still 120 from 1 hot to neutral.

As for how to fix it?  Hire an electrician.  Could you fix it yourself?  maybe.  Could you burn your house down?  maybe.  Could you sleep at night after messing with it yourself?  only just maybe.  Hire a professional for anything that is a combination of dangerous and slightly outside your comfort zone.