"Voting the graveyard" probably refers to what is usually called the "graveyard vote", where people who are actually dead mysteriously turn up as having cast votes on election day. In some especially corrupt districts, the graveyard is apparently one of the ruling party's biggest strongholds.
Logrolling appears to be another name for legislative horse trading. "I'll give you a vote towards banning gay marriage if you'll help my pork barrel scheme get through."