As far as I understand from the discussion here, a "neder" is a vow forbidding or consecrating objects, whereas a "shevua" governs personal actions. For example, one would make a neder to declare wine forbidden to himself, but a shevua to go to work the next day.
1) Why is "bli neder" the common expression for self-exemption from promises when it is almost used in conjunction with shevuot (i.e. "I'll go to the store for you") rather than nedarim? Does this affect its halachic validity as an expression of intent to self-exempt from shevuot?
2) Is there some alternative phrase that might be better used for shevuot per se?