I am at a certain part in my book where a group of six people travel and talk with each other. I would like to make them all talk, as that would be what would happen in real life but I can't really figure out how to specify who is talking without using. "Character said" or "Character noted". Are there any other words then those two or is there even a way to avoid it all together?
Don't use "Character noted." Stick with "Character said." It works perfectly because it gets the job done and because when done right it becomes invisible to the reader.
Try to edit out as many "Character said" as you can without forcing the reader to count lines.
One way to do this is to use action to "indicate who owns the paragraph." I.e. a "Character does something," followed by the dialog without a "said" after.
But as you've noticed, when more than two people are talking and especially when they are talking over each other you need to use other techniques.
In this case, it's not unlikely that the conversation will be so complex a single person (imagine an "I") would not be able to follow it all but would have to focus on some parts and shut other parts out.
Think of it as a camera/microphone covering the dialog. It can only focus on a small part (or an auditory group shot wouldn't be much more than a "murmur of voices").
This focus can move, jump from one conversation to another and even cut things off halfway.
This way you can allow the conversation to split and merge naturally and still cover it on the page.
If you have previously established a speaking style of some of the characters then you can try using dialogue tags only where it is not immediately obvious who is speaking. Sometimes in a group scene it may not be necessary to quantify who said what.
If you have a section where only 2 characters are talking, you could use this to emphasise their speaking style.
Using tags can help you control the flow and pacing of the scene. Try to avoid raiding a thesaurus for tag adverbs if you feel 'said' is being used too much.
Try a few ways of writing the scene and see what flows.
If it is clear which character is speaking(like pincq suggests) you don't need them. You can also establish who is talking in dialogue by referencing their own unique past. Since the others haven't done the event, they can't be the ones saying they did it.
Another reason you might not need them is because it doesn't matter who said it.
If your group is just making small talk, and they're just talking about, say, how much bread costs, then it probably doesn't matter who says it's $3 and who thought it was $2.25. In cases like that, you can leave out dialogue tags since it doesn't really matter who is speaking.
Establish the order and tone of those conversing and then stick to it, your reader will have to pay attention to keep up but you want them to do that anyway. If you have a new character come in part way through make a note of their particular way of speaking by way of introduction "so-and-so's yokel burr cut into X's flow mid-sentence to note ... ". For a number of good examples of conversations that are established and then left to run without further speaker's names read S.M. Stirling's The Protector's War, about a third of the book is a round table meeting with as many as 7 speakers. I recommend the Emberverse series for picking up writing technique in general in fact.