ご機き嫌げん斜ななめ

ご

き

げ

ん

な

め

Meanings

1

in a bad mood; cranky; cross

Polite expression describing someone's foul mood, often used with だ or です. Literally 'honorable mood is slanted'.

The department head is in a bad mood today.

ご機き嫌げん斜ななめの猫ねこに近ちかづかないほうがいい。

You'd better not approach a cranky cat.

機き嫌げんが悪わるい
More direct and less polite; ご機嫌斜め is a softer, euphemistic way to say someone is in a bad mood.
不ふ機き嫌げん
A straightforward noun/adjective meaning 'bad mood'; ご機嫌斜め is more playful and indirect.

From ご (honorific prefix) + 機嫌 (mood, temper) + 斜め (slanting, tilted). The image is of a mood being 'off-kilter' or 'not straight'.