Modern advanced photonic integrated circuits require dense integration of high-speed electro-optic functional elements on a compact chip that consumes only moderate power. Energy efficiency, operation speed, and device dimension are thus crucial metrics underlying almost all current developments of photonic signal processing units. Recently, thin-film lithium niobate (LN) emerges as a promising platform for photonic integrated circuits. Here we make an important step towards miniaturizing functional components on this platform, reporting probably the smallest high-speed LN electro-optic modulators, based upon photonic crystal nanobeam resonators. The devices exhibit a significant tuning efficiency up to 1.98 GHz/V, a broad modulation bandwidth of 17.5 GHz, while with a tiny electro-optic modal volume of only 0.58 $μ{\rm m}^3$. The modulators enable efficient electro-optic driving of high-Q photonic cavity modes in both adiabatic and non-adiabatic regimes, and allow us to achieve electro-optic switching at 11 Gb/s with a bit-switching energy as low as 22 fJ. The demonstration of energy efficient and high-speed electro-optic modulation at the wavelength scale paves a crucial foundation for realizing large-scale LN photonic integrated circuits that are of immense importance for broad applications in data communication, microwave photonics, and quantum photonics.