Text: http://www.stoa.org/diotima/anthology/wlgr/wlgr-greeklegal88.shtml
What would these torches have been made out of? Why wouldn't they use lamps or candles?
The passage you're referring to is Lysias 1.24:
καὶ δᾷδας λαβόντες ἐκ τοῦ ἐγγύτατα καπηλείου εἰσερχόμεθα, ἀνεῳγμένης τῆς θύρας καὶ ὑπὸ τῆς ἀνθρώπου παρεσκευασμένης
And, taking torches from the nearest shop, we went in through the door which the servant girl [literally "the human"] had prepared.
The verb used in relation to the torches is λαμβάνω, to take or seize. The group intent on murdering Euphiletos' wife's lover didn't go to a convenient emporium of angry mob supplies to purchase some torches. Rather, they found a nearby place with torches burning outside, and took them off the wall for their own use. Torches would have been more suitable than oil lamps in this case, because the men were intent on violence. It is not certain whether candles existed in ancient Greece.
The torches themselves would have been made of pine wood, presumably coated in pitch or some other slow-burning substance.