In Sublime Text 3, unicode characters are not shown correctly. In gedit it works fine. I tried saving the document as UTF-8, Tried setting default encoding to UTF-8 but stil
Go to Preferences > Settings > User.
Add this setting:
"default_encoding" : "utf-8",
Sublime doesn't support Complex Text Layout at all I'm afraid. That means you don't even get proper Arabic or Hebrew, let alone Sinhala.
Hopefully this will be added some day but it's not a straightforward feature. As Sublime is focused on code rather than natural language it might not be amongst the author's priorities.
Sublime Text 3 should support many utf-8 locales now.
If Xuwei Khan's answer doesn't work for you, then use this command:
iconv -f Windows-1253 -t utf-8 input.txt > output.txt
Or replace Windows-1253
with an an other iso locale suitable for your language needs.