Motivated by the huge success of Transformers in the field of natural language processing (NLP), Vision Transformers (ViTs) have been rapidly developed and achieved remarkable performance in various computer vision tasks. However, their huge model sizes and intensive computations hinder ViTs' deployment on embedded devices, calling for effective model compression methods, such as quantization. Unfortunately, due to the existence of hardware-unfriendly and quantization-sensitive non-linear operations, particularly {Softmax}, it is non-trivial to completely quantize all operations in ViTs, yielding either significant accuracy drops or non-negligible hardware costs. In response to challenges associated with \textit{standard ViTs}, we focus our attention towards the quantization and acceleration for \textit{efficient ViTs}, which not only eliminate the troublesome Softmax but also integrate linear attention with low computational complexity, and propose \emph{Trio-ViT} accordingly. Specifically, at the algorithm level, we develop a {tailored post-training quantization engine} taking the unique activation distributions of Softmax-free efficient ViTs into full consideration, aiming to boost quantization accuracy. Furthermore, at the hardware level, we build an accelerator dedicated to the specific Convolution-Transformer hybrid architecture of efficient ViTs, thereby enhancing hardware efficiency. Extensive experimental results consistently prove the effectiveness of our Trio-ViT framework. {Particularly, we can gain up to $\uparrow$$\mathbf{7.2}\times$ and $\uparrow$$\mathbf{14.6}\times$ FPS under comparable accuracy over state-of-the-art ViT accelerators, as well as $\uparrow$$\mathbf{5.9}\times$ and $\uparrow$$\mathbf{2.0}\times$ DSP efficiency.} Codes will be released publicly upon acceptance.