'Appugno' means to fight.
Deus is the general term for a god, but remember before latin became a dead language, polytheisim was the general religious practice followed despite the impact of the rapidly spreading mono theism introduced sometime after 306. It would be highly unlikely there would be any who opposed all gods. Although one may fall out of favor to one god there were always others who were benevolent whilist others vengenful.
Polytheism had its roots firmly planted in Greek cultural custom and religious worship until Consantine converted to christianity after becoming emperor of Rome in 306. His conversion to christianity had a huge impact with far reaching effects on common practices of religion of all factions seen even today. At the time of his conversion, he was the most powerful and influential ruler in all the western world. His conversion is quite an interesting story as well.
'Nefastus' could mean unholy. Combine this with 'bellis', wage war, then 'reclamito' meaning to cry out against adding deus and you have something like 'unholy war against the god(s),
'Motus' could be a movement 'impingo' is to drive against and then 'belligero' means to wage war could be put together like 'Motus belligero impingo deus', the movement to wage war against the God(s).
Or you could use any number of combinations. There are a ton of words that could be substituted, but different local dialects of the time combined with varying educational levels of vocabulary and social class would have a lot to do with how it is put together.
Overall, I think the english phrase, "The war against god' doesnt have any real direct translation to latin because in latin, that phrase didnt exist as such.
So for a school project, the assignment may be to find the best words to translate it, but there is no right answer. It is a phrase that exists in many languages today in some form or another, albeit best when describing the assault on the Pledge of Allegiance to the United States of America in school classrooms by athiests. tie that in with the latin translation and you may get an A+.