How do I logout of Hangout on Android 4.4?
https://support.google.com/hangouts/answer/3118600?hl=en

this doesn't work? I haven't tried it, because I don't have hangouts on my phone.

EDIT 1

Sign out of Hangouts

TIP: If you don’t want to receive notifications, enable Snooze notifications.

Touch Menu  >​ Settings > Touch your Google account > scroll to the bottom and touch Sign out.