Select Sri Lanka in http://garmin.openstreetmap.nl, download the osm_generic_gmapsupp.zip file, and unzip it, which gives you a file called gmapsupp.img. Optionally rename it (e.g OSM_Sri_Lanka.img), keeping the '.img' extension so that the GPS knows what it is; that allows you to have more than one supplementary map on recent Garmin devices such as the Oregon. Connect your GPS to a computer, and copy the '.img' file to the Garmin directory, either on the GPS device or on its Micro SD card if you have fitted one. That's all. My Etrex 30 automatically enables any newly downloaded maps in every profile, and I would expect the Oregon to do the same. If it does not, enable the map as nevw describes. You should be able to leave the worldwide basemap enabled (for what it is worth), enabled, as downloaded maps seem to take precedence over the basemap in the regions that they cover. I can't vouch for its behaviour at the edges of the downloaded map, which is another good reason for downloading a map containing the whole of Sri Lanka and much of the surrounding water.
Don't worry about the size of the file. Garmin 'img' files use a vector format, which means that their size depends on the amount of information that they contain, not on the area that they cover; OSM does not contain much information about areas of ocean. The Sri Lanka map is about 1/20 of the size of the map of the United Kingdom, which I keep on my Etrex 30 and update occasionally.