death note...
 

In the live action movie Death Note, Light comes down from upstairs and tells his sister Sayu "be careful of strangers." Then Sayu says "i will." And then she says what sounds like itikimasu. (And then light's mom said something back to Sayu) What does that mean? (if thats even what Sayu said) I was watching death note last night in japanese with no subtitles trying to see how much japanese I could understand. And it didn't sound like "sayounara." (The only way I know how to say goodbye in japanese)

I haven't watched the movie, but she probably said "ittekimasu", which means I'm leaving. :)

Greetings are really difficult to translate into english because they're so context bound. Good on you for working without subs! You should definitely make notes and try and remember phrases too. Remember there's no ti sound really in japanese, so that should have told you that it can't have been 'itikimasu'.

She says 'いってきます’ ittekimasu and her mother responded with いったらっしやい　ittarasshai. These words are a pair that are customarily said when someone is leaving the house. Ittekimasu means literally something like "i go and will come back", but is more like an 'I'm off now, bye!'. Ittarasshai means 'go out and then return' but is more like a 'Take care, see you later!'.

Sayonara is used more in situations where you're not really planning to see the other person in a while, like more than a few days. It's more of a 'farewell' than a casual goodbye.