Both of these (along with the French for “worldly boredom”, ennui) come from the Latin inodiare, meaning, “to hate”. The Latin in- adds emphasis to the odium, Latin for “hate”.
We can see the parallels in all with the open vowel, followed by the -n-, followed by a -y- sound, although in Spanish the -y- sounds (and its corresponding -x- and -sh- variations) often turned into the -j- sounds, as it did here. Thus, the a-n-y maps to the e-n-j.
Hatred, then, dissipates and weakens over time. In English, hatred weakens into mere annoyance. In Spanish, hatred weakens into just anger, enojo. And, best of all, hatred in French weakens into a world-weary boredom of ennui.