Most household electrical symptoms allow time to think. This one does not, and it is worth being clear about why.
The smell people describe as burning plastic or fish comes from the materials used in wiring devices and conductor insulation as they overheat. Those materials are chosen partly because they are flame retardant, and the compounds that give them that property produce a distinctive odour when they get hot. By the time the smell is noticeable, the temperature at the source is already well above anything normal.
The usual cause is a loose connection. Resistance at a poor connection converts electrical energy to heat at exactly that point. Because the heat is generated in a small area inside an enclosed box, it can rise quickly.
The immediate response is to remove power to that circuit at the panel rather than to investigate first. If the specific circuit is not obvious, and the smell is strong, switching off the main is reasonable.
Do not pull the device out to look while it is energised. Do not plug something else in to test whether it still works.
Once power is off, a few observations help whoever looks at it. Which outlet or switch the smell is strongest at. Whether anything was running at the time, particularly a heater, an air conditioner, or anything else with a large sustained draw. Whether the cover plate or the plug of whatever was connected shows any discolouration or deformation.
Related signs that belong in the same category of urgency: any visible browning around the slots of an outlet, any buzzing or crackling from a device or the panel, a cover plate that is warm to the touch, or a plug that has become difficult to insert or remove because the slots have deformed.
Space heaters deserve a specific mention. They draw close to the full rating of a standard circuit continuously, for hours. Older outlets whose contacts have relaxed over decades are frequently not up to it, and the combination is a common origin for exactly this problem.
The circuit stays off until it has been looked at.
Further reading: uzbektilida.org