The Strange watchers are three NPCs present in the audience during the Mime random event. When taken to the event, players appeared on a stage with the mime. There were only three spectators; the Strange Watchers.
The three men seemed to represent the three main gods in Gielinor; Saradomin, Guthix and Zamorak, or individual followers of these due to the colour of their clothing. They also resembled statues of the three gods seen throughout the world.
Another thing to note was that the Saradomin-like character was on the left, the Guthix-like character was in the middle, and Zamorak-like character was on the right; possibly resembling the order-balance-chaos relationship between the Gods.