First of all number 2 is wrong..
On number 3 and 1 it's like;
"It's hard to imagine my doing that crime!" -"doing" here is gerund so "my" is correct but it feels a bit empty because the sentence is reflexive.
"It's hard to imagine me doing that crime!" -This is also correct but used in formal writings mostly.
Myself is a reflexive pronoun so if we use myself here;
"It's hard to imagine myself doing that crime!" -So now it has a disgust like strong emphasis and it is hard to grasp by someone like you. Also while talking it is more fluent, common and reflexive. I would totaly suggest using this myself above all else.
the other possible ways of saying it with different meanings;
"It's hard to imagine, that crime is my doing!" -Also true in construct but has a feeling of self acceptance that the crime is done by you and/or you are making a mockery of that crime!