(けんか) Any kind of fight – from a verbal quarrel to a back-alley stabbing.   $$$
(たたかう) Even more broad than 喧嘩, 戦う can be used about fist-fights, but it’s also commonly used in sports, similar to the English “Go! Fight! Win!”. In that case, it’s not that different from 頑張れ!   $$$
(たたかう) Fight – (only used figuratively) – struggle against temptation, war on poverty etc., the war on drugs, struggle against prejudice, etc.
もみあい Literally, “fondling each other.” Unlike a 戦う (battle), which can go on a long time,  a もみあい breaks out suddently – usually in a place where people are drunk. Close to 喧嘩 but more narrow:it’s a shoving match or fist-fight.
(なぐりあい) Literally, “hitting each other.” 殴り合い is not totally limited to muggings and gang beatings – if you and your friend are drunk and start slapping each other on a dare, that’s also 殴り合い.
(せんとう) A war battle.   NP
(かっせん) Like 戦闘、 but only used in proper nouns:the Battle of the Bulge, The Battle of 1812. The Battle of Pearl Harbor, etc.