Detection of vehicles and their classification is a significant component of wide-area monitoring and surveillance, as well as intelligent- transportation. Existing solutions tend to employ heavy-weight infrastructure and costly equipment, as well as largely depend on constant support from the cloud through round-the-clock internet connectivity and uninterrupted power supply. Moreover, existing works mainly concentrate on localized measurement and do not discuss their efficient integration to address the problem over a wide area. For practical use in an outdoor environment, apart from being technically sound and accurate, a solution also needs to be cost-effective, lightweight, easy to install, flexible, low overhead, and easily maintainable, as well as self-sufficient as much as possible. However, fulfilling all these goals together is a challenging task. In this work, we propose an IoT-assisted strategy, LiVeR, to accomplish it. For self-sufficient on-the-fly classification in resource-constrained low-power IoT devices, LiVeR minimizes not only the computational requirements but also the energy consumption, which enables sustained operation in a hostile outdoor environment for a considerably long time solely based on battery power. Through extensive studies based on outdoor measurement and trace-based simulation on empirical data, we demonstrate that LiVeR classifies vehicles of small, medium, and large size with an accuracy of 91.3% up to 98.8%, 92.3% up to 98.5%, and 93.8% up to 98.8%, respectively, for single-lane traffic. We also demonstrate that LiVeR spends only about one-third of the number of RF packets to achieve vehicle detection and classification compared to the state-of-the-art RF-based solution, considerably extending the lifetime of the system.