I do not know if there is any oil sump for a 2 stroke vehicle and basically it is mixed along with the gasoline. Why is that so in a 2 stroke vehicle. And can we have an oil reservoir or a sump of oil for a 2 stroke vehicle as we have in a 4 stroke vehicle.
Because in a two-stroke, the air-fuel charge gets taken into the crankcase. If there were a sump of oil there, it would get sucked into the engine. There are many two-strokes where the oil is stored separately from the gas and injected at the intake manifold, that is probably the closest you'd get to what you're asking about.
So there are quite a few two stroke engines. For gassers like chain saws, the oil and fuel (gasoline) are mixed and introduced into the crankcase by the carburetor. The oil lubes the engine, and is part of a fuel mix.
Two stroke diesels are common in larger power plants, like stationary generators and marine power plants.
A two stroke automotive engine is normally a two stroke gasoline engine, and the oil for the crankcase is not premixed (except on rather old cars) but is instead injected with the gasoline as it is demanded for power. The injection can work two ways (normally): it can be injected into the gasoline just before the carburetor or fuel injection port, OR it can be injected into the crankcase and is metered according to the power demand. Both these approaches work better for autos than for chainsaws, because there can be better control of the lubrication, and not just a fixed oil ratio for all speeds and power settings.
So, at least as I am aware of, there are no production cars in the US where the gasoline and engine oil are premixed in the fuel tank.
Having said all of that, I recall a couple of years ago that Renault was coming out with a two stroke diesel engine for cars (while not for marine and stationary power plants, it is a different combustion cycle) and this engine would have a sump for lubrication oil. The fuel would be injected into the cylinder during the burn cycle.
Most of my experience with two stroke or two cycle automobile engines was about 40 to 50 years ago, when there were some Saabs which were two cycle gasoline engines. Those injected oil, and had a separate tank for it. We kind of thought of those engines as time bombs, although I saw few that actually died before other things happened to the cars.
To summarize, in a two cycle Otto cycle gasoline engine, the lubrication oil is separately tanked, and is metered into the fuel, or directly into the combustion chamber, based upon power demand and/or RPMS, which is different than the common chain saw or weed whacker two cycle Otto engine, where the fuel and oil charge is premixed, and introduced to the crankcase, typically though a carburetor.
There are in fact two stroke engines that get lubricated by an oil sump / pump system and do not receive the lubricating oil through the air-fuel mix.