As I was driving home, listening to a podcast someone said, “he’s an awfully good guitar player”. That made me think of how the word “terribly” is used in a similar way. I wonder why those two words that if used in the forms of “awful” and “terrible” mean the opposite. Just more craziness of the English language.
Now it bothers me and I pick up on it immediately when I hear those words used in that way. 
If awe and wonder are essentially the same thing, shouldn’t “awful” and “wonderful” mean the same? 
“Awful” and “terrible” both have additional, slightly more archaic connotations of “great magnitude.” One hears in older writing of the “terrible depths” of the sea and the “awful vastness” of the sky.
And a person or thing can be awfully pretty, meaning extremely pleasing to the eye, or pretty awful, meaning somewhat bad. English is fun!
I like words that mean their own opposites. Like ‘overlook’ which can mean ‘did not see’ or ‘make sure to see’, as in ‘scenic overlook’.
Here’s a recent thread from about a year and a half ago on words that mean their own opposite that the OP may find interesting:
“Awful” means “inspiring awe”, but is now almost entirely negative (except in the example you give, I suppose).
“Terrible” means “full of terror” or “inspiring terror”.
I don’t think I have heard “he is a terribly good guitar player” in a positive sense, although “he is a terrible guitar player” parses (but in a negative sense).
“Awful” should probably be synonymous with “wonderful”, but we tend to use “awesome” instead. At some point “inspiring awe” became a negative thing in the word “awful” but remaining positive in “awesome”.
“Awful” is the much older word. I believe once “awful” took on its negative meaning “awesome” was coined to replace it in the positive sense.
Cool is a rule, but sometimes bad is bad. 
( For those that don’t get the reference )
It’s called an auto-antonym.
“Sharp” in the law world has two opposite meanings.
Approving: “Lawyer A is quite sharp on the law” means a lawyer who has a good grasp on the law, including appreciating the nuances that apply in a particular case.
Disapproving: “Lawyer B has a reputation for sharp practice” means Lawyer B is always cutting corners and going just up to the line without crossing it; will screw you on practice points if you’re not careful.
I don’t think those uses are confined to the law.
Not diluting that; just that’s where I come across them the most.
And “frightfully”.
They sound like old-fashioned adjectives posh people use.
Google brings up these quotes of Prince Charles/King Charles III using the phrase “frightfully good”:
And Prince Philip:
Even “bad” can be a general intensifier: “I want that really badly”.
John Finnemore’s Souvenir Programme (sketch comedy on BBC Radio 4) did a wonderful sketch where a grammar snob accosts a clerk for saying that his having exact change is “Awesome!”.
…Or is it your change-making power that brings us all the way to AWEstruck? Young lady, have you been to the Grand Canyon? I can only assume your head would explode.
But then he uses the word “awful” and schadenfreude ensues… the punchline puts the whole thing in perspective.
“Terribly good…” is common enough in some dialects, posh for example (“posh” being a dialect).
John Finnemore is great.
I got his Souvenir Programme stuff (and the best radio comedy series ever, “Cabin Pressure” with Roger Allem and Benedit Cumberbund) from Archive.org.
But the Internet Archive just lost a court ruling, and could be shut down any time. So grab some Finnemore whilst you can.
I don’t think the Internet Archive can get shut down, as long as it’s just providing access to stuff in public domain. Its holdings can certainly be reduced, if I’m understanding the ruling correctly.
I’ll have a listen to the Souvenir Programme. Cabin Pressure is indeed excellent, awfully good, terribly super, utterly fantastic. Like all good comedy it has a poignant touch, like what Captain Martin Crieff discovers when he visits First Officer Douglas Richardson at his home.
I would just add that Robert Falcon Scott’s diary (probably) used the words 'horrible," “terrible,” and “awful” in their earlier meanings.
[quote=From the Diary of Robert Falcon Scott] Wednesday, January 17:
The Pole. Yes, but under very different circumstances from those expected. We have had a horrible day—add to our disappointment a head wind 4 to 5, with a temperature -22°, and companions labouring on with cold feet and hands. . .Great God! this is an awful place and terrible enough for us to have laboured to it without the reward of priority. Well, it is something to have got here, and the wind may be our friend to-morrow. [/quote]
I’m assuming he’s meaning "full of horror, “full of awe,” and “full of terror,” respectively.
Side note: According to one documentary I saw, among all the other problems with the Scott Expedition, the wind was not their friend, and on the way back, the tail wind they were expecting to help push them along either didn’t materialize or became a head wind instead.
For a while, “sick”, normally synonymous with “ill”, was being used by young people to mean really impressive; i.e., “Wow, that skateboarding routine was really sick!”
So was “ill,” for that matter.