The classical demigods, as we understand the term today, are the offspring of an immortal (a god or goddess) and a mortal (a woman or a man). By default they are mortal as their mortal parent, but are more powerful, smart or good-looking than regular humans, as the case may be. (Sometimes tricks or outright divine interventions are used to make them immortal; for example, Hercules, the son of Zeus by the mortal woman Alcmene, was made immortal when an infant by placing him by stealth at the breast of Hera so that he could suck the milk of immortality; he did so, however Hera became aware of the trick and threw him away, in the process spilling a few drops of milk on the sky and creating the Galaxy, the Milk-Stain.)
In their day, the classical demigods used the highest technology available at the time. Homer devotes more than a hundred verses to describe the shield of Achilles (son the mortal man Peleus and the immortal nymph Thetis); Perseus uses mirrors; Bellerophon the flying horse Pegasus; several of the argonauts, travelling on the most advanced ship of the time, were demigods.
Gods and goddesses being immortal and, as Ovid assures us, quite seductive, there is nothing stopping them from making more demigods with modern men and women. Such modern demigods would naturally use the most advanced technology of our days, just as we all do. They would use it better, or be more successful, or something.