No, you can't omit "it". The reason is that "like" is a transitive verb, and a transitive verb MUST have a direct object. In your sentence there is no obvious object that you 'like'. 'It' is therefore an abstract pronoun fulfilling the requirement that there must be an object.
Consider these examples:
1) "I like Jane when she talks to me" - Here Jane is the object I like.
2) "I like smoking when she talks to me" - Here "smoking" is a gerund fulfilling the function of an object.
3) "I like it when she talks to me" - Here, there is no particular THING I like when she is talking to me, so 'it' is a placeholder, but it must be there.
4) "I snore when she talks to me" - Here, 'snore' is an intransitive verb (not requiring an object), so 'it' is not required - in fact, it would be ungrammatical to include it.