Your fourth example seems to not be a real bird.
In “tit(mouse)”, the first syllable comes from an Anglo-Saxon word meaning “small”; hence, “titmase” means small bird. Most of the examples of these birds are referred to as chickadees in the US.
There was no vulgar use of the word “shag” originally, since it came from an old Nordic word meaning “wool”. The species of cormorant referred to would refer to the shaggy appearance of the bird’s crest.
Second last bird named is more commonly known as the northern flicker; the last-named bird is also called the tunki.
Joke is here.
Your head is here.
We have many tufted titmouse birds every day at our feeders. Quite different than the two species of chickadees that also visit daily.