Green’s Dictionary of Slang

1. appalling, awful; esp. as ungodly hour, very late.

1855		Sth Aus. Register (Adelaide) 2 Aug. 2/7: Abercrombie and Biccard, the Esculapius and Galen of the house, accustomed to being ‘kept up’ to the most ungodly hours, were satisfied with a wink.
1868		Dly Ohio Statesman (Columbus, OH) 16 Nov. 3/1: Those who were up at the ungodly and unfashionable hour of two.
1870		Times of india 25 June 2/5: On Thursday evening in London, and at the corresponding time in Bombay (an ungodly hour on Friday morning), a grand telegraphic party took plane in celebration of the completion of the submarine system of telegraphy between India and England.
1887		R.L. Stevenson Merry Men, Olalla in Sel. Short Stories (1980) 186: The wind[’s] [...] ungodly and unintermittent uproar, would not suffer me to sleep.
1999		Guardian 12 Nov. 35: Rodders bells me at his usual ungodly.
2012		J. Duke ‘Bastards of Apathy’ in ThugLit Sept./Oct. [ebook] [S]he would have to wait another ungodly amount of time.
2015		N. Cummins Tales of the Honey Badger [ebook] I swear only one word came out of her mouth before her breakfast quickly followed – ‘Ungodly’.

2. (US campus) extremely good.

1974		Eble Campus Sl. Mar. 6: ungodly – excellent beyond compare.
1977		Fidrych & Clark No Big Deal 146: I’m gonna be so happy walkin’ outa that park. [...] I’m gonna be so happy that it’s gonna be ungodly.