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I'm always horny but so lonely.
Horn may be the reference to its antennae and studies proved cockroaches feel loneliness (Link)
Most women hate me, some even scream at me!
Women hate cockroaches and even scream when they see one.
I might be puny,
Cockroaches are puny.
but don't mock me! I don't have to take this crap! Although I sometimes do.
Cockroaches live in waste, junk and craps.
When a few of us get together we are quite popular!
Might be a reference to 'Oggy and the cockroaches' cartoon series.
Most prefer with fruits, but others prefer my beverage.
Might be a reference to Coke