I know that we usually mutter when we're annoyed, but what about the other situations? I mean, for example, is it odd to use "mutter" instead of "murmur" in the following context?
"I love you," she murmured.
I wanted to clarify this for myself, and I found a good answer on EnglishForums.
'Mutter' is the normal one for 'under his breath'.
'Mutter' is usually complaining to yourself - if you've been told to do something but don't want to, but have to.
'Murmur' is quiet, similar to whisper, but not as conspicuous - for example if you wanted to make an ironic comment to a comapanion when you're meant to be quiet, you might murmur it.
'Mumble' is often used when shy or unwilling to tell someone something - e.g. a young child being told off my a teacher might mumble an answer to a question.
Your example works just fine, but either of these other options could fit better, depending on the greater context.