Please compare their strengths and weaknesses.
I am also curious about what info could come out of attempts at answering this question. Though, I do not like the imperative formulation of the question. It should be a question, not an order.
On the other hand, instead of naming the ORMs at the head of the question, this enumeration should have been done in the body of the question, and it should include more possibilities. That I know, mongomapper, mongoid, activerecord, datamapper, sequel and couchrest are all ruby orms.
Since I have only used ActiveRecord, I cannot answer this question. Though, I have read a little about DataMapper and what I understood is that while ActiveRecord is migration-based and generates the classes according to the database structure, Datamapper does the opposite - that is: it generates the database according to the classes definition.
Additionally, it seems that ActiveRecord and DataMapper are well known orm design patterns: they are well described here: http://msdn.microsoft.com/en-us/magazine/dd569757.aspx#id0400052