Is it awkward to call a wound "heavy"?
I would suggest a deep (if applicable) or serious wound.
EDIT: I wasn't sure about the Ngram link to I attached it as picture, it can be clicked and enlarged. The original ngram is over here: Google Ngram Link for the statistic
Yes, you can describe a wound as "heavy." Google Ngram shows hundreds of examples of "heavy" being used to describe "wound" this way. In fact, there's even an English proverb that says, "A light hand makes a heavy wound." It figuratively refers to the devastation a woman can wreak on a man's heart.
Some examples (emphasis added):
From Crime on the Solent:
I noted the difficulty of accounting for a heavy wound at the back of the head when the man must have been pitched forward, but I supposed it just must have happened.
From The American Mediterranean:
During the fighting he suffered a heavy wound in the chest caused by a bullet fired from close range.
From Hearst's International Combined with Cosmopolitan, Volume 87:
Although the neck arteries and the eyes are protected, it is quite easy and usual for a severe and heavy wound to be inflicted — a wound such as I had just seen.
From Mexican Life: Mexico's Monthly Review, Volume 41:
In contrast, the shot in the thigh had caused a heavy wound.
From The Golden Rule and Odd-fellows Family Companion: Popular Literature, Instruction and Amusement, Volume 6:
The shot inflicted a heavy wound, but not a fatal one...
"Heavy" shouldn't be used as an adjective for the wound, since "heavily" is an adverb meaning "to a large or serious degree". "heavy" and "heavily" are actually completely seperate words, with an obvious shared root.
http://dictionary.cambridge.org/dictionary/english/heavily
You would most commonly describe the wound as "serious" or "very serious", with the latter adding some extra urgency.
The adjective "mortal" can be applied to a wound which leads to the death of the recipient, although this is obviously only used after the person has died (otherwise you're being rather presumptious). It's also perhaps a little archaic. It;s also most commonly used in its adverb form of "mortally", ie "the patient was mortally wounded in the car accident".