We investigate electrical properties of self-assembled branched InAs nanowires. The branched nanowires are catalytically grown using chemical beam epitaxy, and three-terminal nanoelectronic devices are fabricated from the branched nanowires using electron-beam lithography. We demonstrate that, in difference from conventional macroscopic junctions, the fabricated self-assembled nanowire junction devices exhibit tunable nonlinear electrical characteristics and a signature of ballistic electron transport. As an example of applications, we demonstrate that the self-assembled three-terminal nanowire junctions can be used to implement the functions of frequency mixing, multiplication, and phase-difference detection of input electrical signals at room temperature. Our results suggest a wide range of potential applications of branched semiconductor nanostructures in nanoelectronics.