We redid our living room and kitchen last year. We had a HORRIBLE floor to deal with, so we did the area rug thing, and it turned out really well. We got slipcovers for all of the furniture so it matched in something dark but neutral. We painted the living room lavendar, with grayish taupe slip covers in a damask pattern. Then one of the sisters MADE pillows for them, just like on trading spaces :) We got a beige/taupe area rug as well. It turned out really nice. For the kitchen, we painted it butter yellow, and the sister who made the pillows made curtains to match for the windows in both rooms! We put new hardware on all the cupboards and painted them white and put new counter paper on all the counters. Again, it turned out nice! Watch HGTV's Design on a Dime and BBC America's House Invaders. Both give you good cheap ways to fix things up.

Green, beige and purple. One way to incorporate the different colors would be to install a chairrail at about 30-36" high. You could then paint the top of the room a neutral color such as beige and you could use a darker color or wallpaper at the bottom.

You might consider slipcovers and/or curtains in a patterned fabric that incorporates those three colors, then use beige on the walls, and accessorize (pillows, etc.) in purple/violet.
You could also use a green toille that's green pattern on a neutral background for slipcovers or curtains.
Another thing you might consider doing is this...this summer I helped a friend of mine paint her dining room. She painted the walls a taupey-grey and painted the ceiling a silvery-violet. It turned out really nice.

Also, watch the Christopher Lowell Show on Discovery Channel during the week. He has lots of helpful ideas.

Geez, I watch too much home improvement tv!