We extend our formerly proposed theory for non-Born-Oppenheimer electronic and nuclear wavepacket dynamics within on-the-fly scheme [T. Yonehara, S. Takahashi, and K. Takatsuka, J. Chem. Phys. 130, 214113 (2009)] to a case of nonadiabatic dynamics under an intense laser field: electron wavepacket in a molecule is propagated in attosecond time-scale along non-Born-Oppenheimer nuclear paths that smoothly branch due to nonadiabatic coupling and/or optical interactions. Such branching paths are determined consistently with the motion of the electron wavepackets. Furthermore, these nuclear paths are quantized in terms of Gaussian wavepackets (action decomposed function), which can be applied to nonclassical paths. Both electronic wavepacket dynamics and quantization of non-Born-Oppenheimer paths are generalized so as to include the direct effects of the classical vector potential of electromagnetic fields. In the second half of this paper, we perform numerical studies to explore nonadiabatic dynamics in a laser field by examining two cases: one is a two-state model system having an avoided crossing, and the other is two-state dynamics in HF molecule on the two low lying ab initio potential curves. Both are placed in laser fields. With the former system, we survey some basic properties of the coupling of nonadiabatic dynamics and laser interaction varying the relevant coupling parameters such as the laser timing with respect to the incident of nonadiabatic transition. This investigation will set a foundation for the future studies of control of electronic states in realistic multidimensional molecular systems. Application to the latter system shows that non-Born-Oppenheimer quantum chemistry in laser fields is indeed useful in the study of dynamics in ab initio level. Through the comparison with full quantum data, we verify that the formalism and methodology developed here work accurately. Furthermore, we attain some basic insight about the characteristics of molecules in laser fields.