1. Paul visited me in order to ask for a help.
2. Paul visited me in order to ask for help.
(Which one is correct? Are both grammatical? What is the difference between them?)
2 is correct; 1 is not. You wouldn't use "a help" in this context because it cannot be counted (is not a "count noun").
http://grammar.ccc.commnet.edu/grammar/noncount.htm