Low-grade roads often experience frequent roadside intrusions, leading to serious conflicts and disorder. Accurate prediction of the complex traffic-behavior characteristics on such roads is essential for understanding the mechanisms of traffic accidents influenced by roadside intrusions. For this purpose, we collected videos depicting five types of common roadside intrusions on low-grade highways and urban roads. From these videos, we extracted high-resolution vehicle micro-trajectories, and determined the vehicle speeds as they traversed the intrusion area. Then, we identified characteristic sections within the intrusion area, and analyzed the evolution of spatial and temporal characteristics of the vehicle speed. Finally, we established a vehicle speed prediction model using linear, logarithmic and cubic regressions. Notably, the cubic regression model exhibited superior speed prediction performance in the complex scenarios of the intrusion area. The results showed that speed reduction in the intrusion zone of low-grade urban roads is typically higher than that on highways. The deceleration effect is significant for drivers approaching the intrusion source. Additionally, drivers tend to accelerate through the front intrusion zone when their intentions align with those of the intrusion source. However, in scenarios where predicting the behavioral intentions of the intrusion source is challenging, speed may fluctuate to some extent.