We report experimental investigation of the resistivity and Nernst effect in two-dimensional (2D) NbSe2 crystals. A strongly enhanced Nernst effect, 100 times larger than that in bulk NbSe2, caused by moving vortices is observed in thin film. It is found that in the low temperature, high magnetic field regime, pinning effects show little dependence on the thickness and resistivity of the superconductor films. Strong Nernst signals persist above the superconducting transition, suggesting that the Nernst effect is a sensitive probe to superconducting fluctuations. A magnetic field induced superconductor--insulator transition (SIT) is evident, which is surprising in that such a SIT usually takes place in disordered dirty superconductors, while our samples are highly crystalline and close to the clean limit. Hence, our results expand the scope of SIT into 2D crystal clean superconductors.