We investigate magnetoelectric coupling and low-energy magnetic excitations in multiferroic $alpha$-Cu$_2$V$_2$O$_7$ by detailed thermal expansion, magnetostriction, specific heat and magnetization measurements in magnetic fields up to 15~T and by high-field/high-frequency electron spin resonance studies. Our data show negative thermal expansion in the temperature range $leq 200$~K under study. Well-developed anomalies associated with the onset of multiferroic order (canted antiferromagnetism with a significant magnetic moment and ferroelectricity) imply pronounced coupling to the structure. We detect anomalous entropy changes in the temperature regime up to $sim 80$~K which significantly exceed the spin entropy. Failure of Gruneisen scaling further confirms that several dominant ordering phenomena are concomitantly driving the multiferroic order. By applying external magnetic fields, anomalies in the thermal expansion and in the magnetization are separated. Noteworthy, the data clearly imply the development of a canted magnetic moment at temperatures above the structural anomaly. Low-field magnetostriction supports the scenario of exchange-striction driven multiferroicity. We observe low-energy magnetic excitations well below the antiferromagnetic gap, i.e., a ferromagnetic-type resonance branch associated with the canted magnetic moment arising from Dzyaloshinsii-Moriya interactions. The anisotropy parameter $tilde{D}=1.6(1)$~meV indicates a sizeable ratio of DM- and isotropic magnetic exchange.
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