Strings can make a difference, however, this varies greatly depending on what you're talking about. Strings types can effect feel, power, spin, and how your physical arm feels. Tension of string has the greatest effect on these. It's difficult to judge strings sometimes because a strings often play better at different tensions then perhaps the normal say 60lbs you've always strung at. Gage of the string also plays a role. Typically I've found that I look to different strings when I'm concerned with durability and feel at impact. As far as cheap vs expensive a lot of times I gravitate towards even cheap synthetic gut because the little extra I might notice in spin etc is so minimal that it's not worth paying 3 times as much for it.
Bottom line I think too many people believe a racquet or string will magically make them play better or add an element to their game they don't have. In each case the new element usually means you sacrifice something else (power for control, etc). The best racquets and string are those that compliment your swing style, swing speed, game style, prefernce for feel and spin the most. If it complements you and how you play then you'll have more confidence and hence play better. To improve your game you just need to work that aspect. Don't let a low price of string make you think that it's unworthy or that you'll play better with something more expensive.