What are the sociological research methods?

Depends. There is research, and development of research. Research development methods are consistent with Psychological methods. Exempli gratia, chi square, and correlation coefficient. So, statistics.

Research methods include archival research, surveys, unobtrusive observation, participant observation, utilization of control groups, and experimental groups. Back in the day, some very important research was done using participant observation over several decades. To me, this is the backbone of Sociological research. Time consuming data compilation and comparison.

For some great examples of data collection and theory development, research Max Weber (The Protestant Ethic and the Spirit of Capitalism), Talcott Parsons (Cybernetic Social System), and Herbert Blumer (Proponent of symbolic interaction, and social trend analyzer).

If you would like an accurate definition of the Words I used, grab a copy of "Sociology: The Core" by Michael Hughes, et al. Chapter one has the definitions.