They all have the same meaning, but their use is not necessarily interchangeable - it depends on the context:
The company promised to "abide by" the terms of the laws of work. (Formal - often seen in legal documents)
The company promised to "keep to" the terms of the laws of work. (Standard, everyday speech)
The company promised to "stick to" the terms of the laws of work. (Informal, almost slang...)