there is an interesting article written by fr. Basil Mahfoud in Arabic "الجهاد والاستشهاد في الفكر المسيحي" that's in English "Jihad and martyrdom in Christian thought".
And, remembering that Arabic is a Semitic language, so based on roots and derivates (subjects) from them, both the priest (in the second paragraph of the article) and root-dictionaries (e.g Wehr) claim it's from root جهد
connected with effort, strain, stive, work etc. And this word is used in Arabic Orthodox works as an equivalent of Church Slavonic podvig
(подвиг). Surely, in Islam context this effort is understood in different manner.