You should make this your friend:
A Glossary of Key Words (HSC) - Board of Studies NSW
and from that-
Analyse:Identify components and the relationship between them; draw out and relate implications
Evaluate:Make a judgement based on criteria; determine the value of
Critically (analyse/evaluate):
Add a degree or level of accuracy depth, knowledge and understanding, logic, questioning, reflection and quality to (analyse/evaluate)
those are the official definitions, if you want a working definition:
Analyse: Is well...analysis. You talk about important components (aspects of whatever issue), you analyse the relationship between those components such as the causes and effects, what leads to what, the imacts and results.
Evaluate: Is a higher level of analysis where you make a judgement, such as (history) who's fault was it?, or (economics) what feature of the economy lead to X problem? or even (english) which text conveys X better?
Critically: You just evaluate/analyse to a greater degree, more detail, or dealing with more sophisticated concepts, perhaps different or more conceptual levels of analysis.