I believe the purpose of those tweets was to be funny. I believe he was trying to be funny, in all three situations.
Joke 1: Scot's drink a lot.
Joke 2: I'm actually not even sure where the punchline is in this tweet, it's really just a bad joke from a writing standpoint. Still, despite my best efforts, I cannot isolate a single piece of that tweet that is offensive to the homosexual community. (I heard on Rosaforte's report that Elkington claims he was making a joke about how much ESPN was covering Michael Sam. This actually sounds like a plausible explanation to me. In fact, I've heard this joke before. People make the same joke for Tiger, LeBron, and Brady...its like: hahaha, look how much ESPN sucks up to ________, so much so that we now know what he ate for breakfast, wears for underwear, or e.g. how many times LeBron dribbles the basketball per second.)
Joke 3: Stephanie, you are short and have small boobs. Probably the funniest of Elk's jokes, although the humor is cheap and Seinfeld certainly wouldn't put it in his set.
Alright, you're right he's not well liked to begin with so it might be wise for him to just abstain from tweeting to avoid all confusion.
But, when we look at his comments from an objective standpoint it is illogical (and unfair) to conclude that Elk is : A) apathetic towards death by heli crash, B) a homo-phobe or bigot, or C) a sexist or "heightist" ;).