They actually explained how he got out of all these situations:
- Eddie Morra was at the apartment just before and after the murder of Vernon Gant. He also called the police.
Gant was a known drug dealer and so it's not unlikely for him to have enemies. Eddie was his ex-brother-in-law, so it's not too strange that he would show up at his apartment. The police interviewed him, but there was no evidence for his involvement.
- Eddie Morra was at the hotel-room when the "blonde" was murdered.
There was a witness who identified Eddie in a picture from a newspaper article. At this point Eddie gets help from one of the best attorneys in criminal law, who manages to get him off by setting up the police lineup with a bunch of Eddie-look-alikes, so that the witness cannot identify him. Later we find out that the lawyer was actually sent to steal his NTZ stash.
- Gennady and his Russian's associates were killed in Eddie Morra's apartment.
This was explained as well. The police came to the conclusion that the Russians were actually looking for an earlier owner of the loft, who was an arms dealer. It's likely that Eddie gave them that idea with some help of NTZ.