Topological metals exhibit unremovable degeneracies in the band structure close to the Fermi level. These degeneracies can come in many types, the most basic of which are point (Weyl) and line nodes, and are associated with a wide range of phenomena from chiral anomalies to Fermi arcs. Here we show that MoTe2, in its low-temperature orthorhombic structure, realizes both type-II Weyl points and nodal lines close to the Fermi level, in a complex topological band structure. The Weyl nodes occur between several different bands, and the nodal lines are protected by mirror symmetry. We present an X-ray diffraction study of this new orthorhombic phase of MoTe2 taken at 100 K, and experimentally determine its lattice parameters. Using this input in ab initio and topological calculations, we predict a series of strain-driven topological phase transitions in this compound, opening a wide range of possible experimental realizations of different topological semimetal phases. Crucially, with no strain, the number of observable surface Fermi arcs in this material is 2 - the smallest number of arcs consistent with time-reversal symmetry.