Are the three sentences correct and do they have the same meaning?
The traffic started to move when the police had cleared the road.
The traffic started to move after the police had cleared the road.
The traffic started to move once the police had cleared the road.
...ONCE the police had cleared the road. This means that traffic started to move IMMEDIATELY after the police cleared the road. There was little/no waiting. "Once" implies that there is no need to wait.
Understandable, but not best:
...WHEN the police had cleared the road. I would rearrange this: "When the police had cleared the road, the traffic started to move." This is OK, but not great. WHEN does not necessarily imply connection. In fact, it often implies surprise or unexpectedness. For example, "I was walking down the street when it suddenly started to rain!"
"When" can simply mean that two things happened at the same time. It does not NECESSARILY mean one event CAUSED the other.
...AFTER the police had cleared the road. This is OK. However, "after" does not give any sense of how long the wait was. In the context of the story about traffic and police, I could probably figure it out. But it is not perfectly clear.
Again, "once" is probably the best choice. The others are understandable, but not precise.