Well, Plato says, ἔρως δέ, ὅτι εἰσρεῖ ἔξωθεν (PL. Crat. 420a), in fact it is not exclusive ox sexual desire, for instance,
αὐτὰρ ἐπεὶ πόσιος καὶ ἐδητύος ἐξ ἔρον ἕντος (IL. I, 469) (when they had fulfilled their desire of drinking and eating).
For the oder two, always Plato says; καὶ μὴν πόθος αὖ καλεῖται σημαίνων οὐ τοῦ παρόντος εἶναι (ἱμέρον τε καὶ ρεύματος) ἀλλὰ τοῦ ἄλλοθι που ὄντος καὶ ἀπόντος, ὅθεν πόθος ἐπωνόμασται ὃ τότε, ὅταν παρῇ οὗ τις ἐφίετο, ἵμερος ἐκαλεῖτο· ἀπογενομένου δὲ ὁ αὐτὸς οὗτος πόθος ἐκλήθη. (PL. Crat. 420a) (pothos, instead is called this way to signify that it is a wish of something that is not present, but is far away, and it is for this reason that it has been called pothos, then, when that of which somebody had a desire is present, it is called imeros.).
In effect, also this is not exclusively a sexual desire, for instance,
ἡνιόχοιο πόθος. (IL. XVII, 439) (wish of the horse-driver, that is the wish of the horses for their driver, Automedonte), and,
τῷ δ'ἄρα πατρὸς ὑφ'ἵμερον ὦρσε γόοιο, (OD. IV, 113).