The payment plugins have their language files in the administration section. So instead of directly editing the language files, you can translate the strings via the language override feature of Joomla.
Here is a step by step tutorial.
Go to Joomla administrator->Language Manager->Overrides.
IMPORTANT: You must set the Filter to Administrator as shown in the screenshot below before creating an override.
Set filter to Administrator as shown in the below image. (NOTE: If you are not an English user, you should choose your language)
Now, Click New to create an override.
For example, you want to translate: K2STORE_MONEY_ORDER
Fill up the override form
Language Constant : K2STORE_MONEY_ORDER
Text: Your translation
Now click save.
NOTE: If you do not know the language constant to translate, you enter the text to be translated in the Search box on your right side of the screen and get the Language constant.
You may also want to read this article: http://k2store.org/support/documentation/item/46-howto-write-a-language-override.html