@beamerguide

Advantages----

• 2-stroke engines have a significant power boost/supply than a 4-stroke engine as it is fired every 2 revolution and hence can produce double power than a 4-stroke engine.
• 2-stroke engine is lighter in weight due to simple construction than 4-stroke engine. as it don't have any mess with valves or we can say it don't have valves.
• A typical 4-stroke engine can't work in any orientation, in order to resolve it more complexities would be added to it. But in case of 2-stroke engine it will work in any orientation given.
• 2-stroke engines generate more power than 4-stroke engine
• Moreover 2-stroke engines are less expensive than 4-stroke engine.

Disadvantages----

• We all know that 2-stroke engine stroke engine require 4-stroke oil mixed with gas, in order to lubricate the crankshaft, It not only burns gas but also the  2-stroke engine oil with it.
• So 2-stroke engine oil adds to the cost of gas. Hence it becomes very much expensive.
• 2-stroke engines worn out very early than  4-stroke engines due to lack of dedicated lubricating system.
• Sometimes even gas leaks out of the exhaust valve of 2-stroke engine, leading to storage of gas.
• 2-stroke engine not uses the gas efficiently, leading to decrease in mileage of the system.
• 2-stroke engine produces a lot of pollution with it, leading to many environmental pollution.

Actually 2-stroke engine work in a very similar way to that of 4-stroke engine. Only there's a difference between the number of strokes or no. of cycles.

In a 2-stroke engine-

Demonstration Of Two Stroke Engine's Working

First-stroke:
The piston comes down and pressurizes the mixture of oil/air/gas upwards into the combustion chamber, this displaces the extra exhaust.

Now comes the most important stroke i.e. the Second stroke or Compression stroke:
Now the piston moves up, towards the spark plug this creates a vacuum in the crankcase and opens the inlet port & sucks the mixture into the crankcase from the carburetor. Here the piston compresses the mixture which it got in First stroke, the Spark plug ignites the mixture. This drives the piston back and the cycle continues....
See the Diagram while reading this would help you a lot.

In a four-stroke engine, there are separate intake, compression, combustion and exhaust strokes.
You can see here, intake and combustion is occurring at the same time, moreover instead of taking 4-stroke, it is burning the gas in just 2-stroke/cycles. These advantages make two-stroke engines lighter, simpler and less expensive to manufacture. Two-stroke engines also have the potential to pack about twice the power into the same space because there are twice as many power strokes per revolution. The combination of light weight and twice the power gives two-stroke engines a great power-to-weight ratio compared to many four-stroke engine designs.