In spite of the recent success of Dialogue Act (DA) classification, the majority of prior works focus on text-based classification with oracle transcriptions, i.e. human transcriptions, instead of Automatic Speech Recognition (ASR)'s transcriptions. In spoken dialog systems, however, the agent would only have access to noisy ASR transcriptions, which may further suffer performance degradation due to domain shift. In this paper, we explore the effectiveness of using both acoustic and textual signals, either oracle or ASR transcriptions, and investigate speaker domain adaptation for DA classification. Our multimodal model proves to be superior to the unimodal models, particularly when the oracle transcriptions are not available. We also propose an effective method for speaker domain adaptation , which achieves competitive results.