Swollen nematic elastomers unconstrained by electrodes exhibit macroscopic deformation as well as an almost full (90 degrees) rotation of director in fast response to sufficiently high electric fields normal to the initial director. The deformation is strongly coupled to the director rotation: The deformation takes place dominantly in the plane where the director rotates whereas almost no dimensional variation occurs in the direction irrelevant to the director rotation. There exists a threshold for the onset of director rotation which is determined by field rather than voltage. The constraint by electrodes prohibiting strain along the field axis strongly suppresses the director reorientation and also significantly increases the threshold field. As the cross-linking density decreases, the electrooptical and electromechanical effects become larger and the threshold decreases. The compressive strain along the initial director axis linearly varies with sin(2) theta (theta: rotation angle of director) in good agreement with the prediction of the soft deformation theory for thin films.