Just to add a bit to the other good answers...
Although the OED notes that the word awful means "Objectively: awe-inspiring"1, the earliest (c8852, approximately 500 years before the advent of offal into the language3) attestation for awful is actually in the sense
- Causing dread; terrible, dreadful, appalling.
This sense of the word has been in continuous use ever since. The earliest semi-positive sense of the word is not attested until c1000, and even then it is more in the sense of "scary" than "awesome":
- Worthy of, or commanding, profound respect or reverential fear.
It is not until the mid-17th century that we get the sense
- Solemnly impressive; sublimely majestic.
(And slightly earlier—by the end of the 16th century—we have the sense "filled with awe", definitions 5 & 6.)
This entry of the OED has not been fully updated, but I suspect that senses 3, 5, and 6 will be listed as now rare or obsolete when it is updated.
By the start of the 19th century, we have examples of the sense
- a. slang Frightful, very ugly, monstrous; and hence as a mere intensive deriving its sense from the context = Exceedingly bad, great, long, etc.
which may be the most common meaning nowadays, and which I take to be the subject of the question. However, this seems to be a fairly straightforward expansion of the original sense of the word, rather than inspired by the word offal. Compare terrible (inspiring terror), horrible (inspiring horror), dreadful (inspiring dread), and tremendous (inspiring trembling) and their adverbial forms, which acquired their colloquial and intensifying usages around 1500, 1500, 1700, and 1800, respectively without any homophonic influences.
1 "awful, adj." OED Online. Oxford University Press, March 2017.
2 At this time the word was actually ęgefull, an Old English cognate of the word which became our modern awful; however, the two root words (for awe)
were practically treated as dialectal variants of the same word, of which aye was still used in s.w. c1400, while awe was in the n.e. c1250. The sense-development is common to both. They are therefore here taken together; the examples being separated into groups α(from Old English ęge) and β(from Old Norse agi).
3 First attested ▸a1398. ("offal, n. and adj.")