A key challenge in quantum computation is the implementation of fast and local qubit control while simultaneously maintaining coherence. Qubits based on hole spins offer, through their strong spin-orbit interaction, a way to implement fast quantum gates. Strikingly, for hole spins in one-dimensional germanium and silicon devices, the spin-orbit interaction has been predicted to be exceptionally strong yet highly tunable with gate voltages. Such electrical control would make it possible to switch on demand between qubit idling and manipulation modes. Here, we demonstrate ultrafast and universal quantum control of a hole spin qubit in a germanium/silicon core/shell nanowire, with Rabi frequencies of several hundreds of megahertz, corresponding to spin-flipping times as short as ~1 ns - a new record for a single-spin qubit. Next, we show a large degree of electrical control over the Rabi frequency, Zeeman energy, and coherence time - thus implementing a switch toggling from a rapid qubit manipulation mode to a more coherent idling mode. We identify an exceptionally strong but gate-tunable spin-orbit interaction as the underlying mechanism, with a short associated spin-orbit length that can be tuned over a large range down to 3 nm for holes of heavy-hole mass. Our work demonstrates a spin-orbit qubit switch and establishes hole spin qubits defined in one-dimensional germanium/silicon nanostructures as a fast and highly tunable platform for quantum computation.