I'm not familiar with those particular components. Just guessing here, but do you have a 7 speed freewheel in the back with down tube shifters? Or it could be a cassette instead of a freewheel check at www.sheldonbrown.com for the difference if you don't know.
Is the shifter for the back indexed, a click-stop for each cog (gear)?
It's possible that the chain and cogs are worn out and need to be replaced. Fortunately those are not really expensive.
Try measuring the chain for stretch. A foot of chain should measure 12 inches over a 24 pin interval. Use a good steel ruler and measure any 24 pin interval.
You may need to take it to a bike shop for help.