Initialization vectors and salts are called such, and not keys, precisely because they need not be kept secret. It is safe, and customary, to encode such data along with the encrypted/hashed element.
What an IV or salt needs is to be used only once with a given key or password. For some algorithms (e.g. CBC encryption) there may be some additional requirements, fulfilled by chosing the IV randomly, with uniform probability and a cryptographically strong random number generator. However, confidentiality is not a needed property for an IV or salt.
Symmetric encryption is rarely enough to provide security; by itself, encryption protects against passive attacks, where the attacker observes but does not interfere. To protect against active attacks, you also need some kind of authentication. SJCL uses CCM or OCB2 encryption modes which combine encryption and authentication, so that's fine. The "authentication strength" is the length (in bits) of a field dedicated to authentication within the encrypted text; a strength of "64 bits" means that an attacker trying to alter a message has a maximum probability of 2-64 to succeed in doing so without being detected by the authentication mechanism (and he cannot know whether he has succeeded without trying, i.e. having the altered message sent to someone who knows the key/password). That's enough for most purposes. A larger authentication strength implies a larger ciphertext, by (roughly) the same amount.
I have not looked at the implementation, but from the documentation it seems that the SJCL authors know their trade, and did things properly. I recommend using it.
Remember the usual caveats of passwords and Javascript:
Javascript is code which runs on the client side but is downloaded from the server. This requires that the download be integrity-protected in some way; otherwise, an attacker could inject some of his own code, for instance a simple patch which also logs a copy of the password entered by the user somewhere. In practice, this means that the SJCL code should be served across a SSL/TLS session (i.e. HTTPS).
Users are human beings and human beings are bad at choosing passwords. It is a limitation of the human brain. Moreover, computers keep getting more and more powerful while human brains keep getting more or less unchanged. This makes passwords increasingly weak towards dictionary attacks, i.e. exhaustive searches on passwords (the attacker tries to guess the user's password by trying "probable" passwords). A ciphertext produced by SJCL can be used in an offline dictionary attack: the attacker can "try" passwords on his own computers, without having to check them against your server, and he is limited only by his own computing abilities. SJCL includes some features to make offline dictionary attacks more difficult:
- SJCL uses a salt, which prevents cost sharing (usually known as "precomputed tables", in particular "rainbow tables" which are a special kind of precomputed tables). At least the attacker will have to pay the full price of dictionary search for each attacked password.
- SJCL uses the salt repeatedly, by hashing it with the password over and over in order to produce the key. This is what SJCL calls the "password strengthening factor". This makes the password-to-key transformation more expensive for the client, but also for the attacker, which is the point. Making the key transformation 1000 times longer means that the user will have to wait, maybe, half a second; but it also multiplies by 1000 the cost for the attacker.