I've seen a couple blog posts and forum threads lately about alignment languages. Some people are doing some interesting things to personalize the concept for their campaigns; others are just arguing whether or not the basic concept makes sense.
I'm going to avoid the latter, but wanted to present the general way I interpret them in my campaigns. My alignment tongues are not really languages, which explains why I specifically call them "tongues", to distinguish them. Instead, they're more like a style of speech, somewhat similar to what in linguistics is known as a register. I do add a slight spin on the concept in that there are certain seemingly ordinary words (in the Common Tongue) that receive unusual emphasis or intonation for an alignment tongue; a modern example would be the way some writers capitalize words like The One, The Way, The Light, The Truth, etc. Sometimes, you even hear someone report how when a particular person spoke, they could "hear the capitalization" in the way that person added stress or inserted pauses before certain important words.
It's not just vocabulary and speech style, however, but also sincerity. Your average person probably knows what the major hot button issues and jargon terms are for any given alignment, but if they tried to pass themselves off as a member of that alignment, their lack of sincere belief in the goals of Law or Chaos will give them away eventually. If you can get someone to talk about religious or moral matters, you will eventually recognize whether or not they are the same alignment. You can never be sure of their alignment if they aren't the same alignment, however; if they use a code word from another alignment, they might be trying to fake it, or it might be a coincidence, and if they don't use the same alignment tongue as you, maybe it's just because they don't trust you. All an alignment tongue guarantees (sort of) is whether someone trying to convince you that they share your beliefs is actually sincere or not.
I said "sort of", because of the assassin issue: assassins can speak other alignment tongues. This makes sense in the context of registers; they basically have the ability to fake sincerity. The assassin is a trained actor, in contrast to non-assassins, which is also why non-assassins can't learn alignment tongues as if they were foreign languages. Registers also explain why a character who changes alignment suddenly "forgets" one alignment tongue and "learns" another. It's not a matter of learning or forgetting anything, but a change in how the character feels; they just can't say "I am a servant of the Light" anymore and really mean it.
Other than convincing comrades in the Cause that you're one of them, there's not much else you can do with an alignment tongue. You can't provide directions to travelers or ask for details about an artifact. One thing you can do, however, is indicate that you sincerely believe that what you are saying is important to the Cause. I think I'd go as far as to allow secret communication between the co-aligned on how someone or something relates to the Cause; other witnesses recognize that you're talking about the local duke, for example, but they don't catch on that you're suggesting the duke is an enemy of Chaos and ought to be "taken care of".
Since I use the simple Law/Chaos alignment system and consider "neutral" to be unaligned, I wouldn't allow a "Neutral Tongue". That would just be the Common Tongue without any secret emphasis on words.