I am interested in obtaining ocean wave data (preferably from actual measurements), such as wave height, period, and direction, in the Southeast Asian region. Where can I obtain them?
The only open and ongoing data source for in-situ ocean wave measurements I am aware of is the National Data Buoy Center. Though NDBC manages data service from plenty of moored buoys in the Gulf of Mexico and the Atlantic and Pacific coasts of North America, unfortunately there isn't much in your region of interest.
The only buoys I have found that are somewhat near the Southeast Asian region are 2 buoys on the east and west side of Guam, and one right by Northern Mariana Islands:
These buoys provide directional energy spectrum data, as well as integrated quantities like significant wave height and mean and dominant wave period. I've written a Python library that lets you parse NDBC server and access data from buoys from command line or your Python programs. Once I tidy it up and make it public, I will update this answer so that other people can use it.
Your other option, as suggested by @DeerHunter, is to use altimetry data from polar-orbiting satellites. Although these are sparse and provide only wave heights (no period or direction information), they may be your only bet depending on the region of interest.