  We study theoretically a three-mode optomechanical system where two
mechanical oscillators are coupled to a single cavity mode. By using two-tone
(i.e. amplitude-modulated) driving of the cavity, it is possible to couple the
cavity to a single collective quadrature of the mechanical oscillators. In such
a way, a back-action-evading measurement of the collective mechanical
quadrature is possible. We discuss how this can allow one to measure both
quadratures of a mechanical force beyond the full quantum limit, paying close
attention to the role of dissipation and experimental imperfections. We also
describe how this scheme allows one to generate steady-state mechanical
entanglement; namely, one can conditionally prepare an entangled, two-mode
squeezed mechanical state. This entanglement can be verified directly from the
measurement record by applying a generalized version of Duan's inequality; we
also discuss how feedback can be used to produce unconditional entanglement.
