Using Raman spectroscopy, we investigate the lattice phonons, magnetic excitations, and magneto-elastic coupling in the distorted triangular-lattice Heisenberg antiferromagnet alpha-SrCr2O4, which develops helical magnetic order below 43 K. Temperature dependent phonon spectra are compared to predictions from density functional theory calculations which allows us to assign the observed modes and identify weak effects arising from coupled lattice and magnetic degrees of freedom. Raman scattering associated with two-magnon excitations is observed at 20 meV and 40 meV. These energies are in general agreement with our ab-initio calculations of exchange interactions and earlier theoretical predictions of the two-magnon Raman response of triangular-lattice antiferromagnets. The temperature dependence of the two-magnon excitations indicates that spin correlations persist well above the Neel temperature.