If you have studied the basic 11th standard thermodynamics you might be knowing the Kelvin Planck statement of 2nd law of thermodynamics.
It states that 'It is impossible to construct any engine that will exchange heat with a single source and convert the complete energy supplied into work'.
An automobile engine is also the same engine described in the statement working on Otto or Diesel cycle.
Now as you asked for a single stroke engine, the possibility is denied by the statement itself so no use of further discussion.
You need to perform 4 fundamental operations of suction, compression, expansion and exhaust to generate work from an engine. For a 3 stroke engine you need to select only 3 of them leaving any 1 operation. Thus practically it is not possible to produce power by executing the 4 operations in only 3 strokes. In a 2 stroke engine, as you may know, suction and exhaust are performed together at the end of the expansion stroke and the 2 strokes performed are compression and expansion respectively. While in a 4 stroke engine the 4 operations are executed consecutively in each stroke. Thus, in my opinion, it is not possible to have a 3 stroke engine. However one such engine is patented in USA but it is not actually a 3 stroke engine but is a 2 stroke engine in reality.