Scale-dependent and geometrical statistics of three-dimensional incompressible homogeneous magnetohydrodynamicturbulence without mean magnetic field are examined by means of the orthogonal wavelet decomposition. The flow is computed by direct numerical simulation with a Fourier spectral method at resolution 5123 and a unit magnetic Prandtl number. Scale-dependent second and higher order statistics of the velocity and magnetic fields allow to quantify their intermittency in terms of spatial fluctuations of the energy spectra, the flatness, and the probability distribution functions at different scales. Different scale-dependent relative helicities, e.g., kinetic, cross, and magnetic relative helicities, yield geometrical information on alignment between the different scale-dependent fields. At each scale, the alignment between the velocity and magnetic field is found to be more pronounced than the other alignments considered here, i.e., the scale-dependent alignment between the velocity and vorticity, the scale-dependent alignment between the magnetic field and its vector potential, and the scale-dependent alignment between the magnetic field and the current density. Finally, statistical scale-dependent analyses of both Eulerian and Lagrangian accelerations and the corresponding time-derivatives of the magnetic field are performed. It is found that the Lagrangian acceleration does not exhibit substantially stronger intermittency compared to the Eulerian acceleration, in contrast to hydrodynamic turbulence where the Lagrangian acceleration shows much stronger intermittency than the Eulerian acceleration. The Eulerian time-derivative of the magnetic field is more intermittent than the Lagrangian time-derivative of the magnetic field.