Solenoids are frequently used for focusing low-energy beams. In this paper, we show how they can serve as multipurpose diagnostics tools to measure various beam parameters, including energy, emittance, the second moments of the transverse distribution, and the beam position and angle with respect to the solenoid's axis. The energy measurement is based on rotation of the plane of the transverse motion, as opposed to generating dispersion with a dipole. Measurement of the beam trajectory with respect to the solenoid axis is done by analyzing the beam orbit downstream of the solenoid while varying its current. The second moments are calculated by analyzing the beam image on a profile monitor while accounting for the beam rotation caused by the solenoid. We describe in detail the corresponding procedures and the experimental results of these measurements.