In one sense, every language is serializable: record someone speaking or signing it, then encode that video into whatever format you like, and now it's been turned into a string of bits. But that's not a very interesting answer.
According to many theories, all spoken languages are fundamentally linear: they're made up of a linear sequence of phonemes, one after another. There are never multiple independent phonemes happening at once (*). So these languages are always serializable.
Signed languages are more complicated. In most signed languages, you can have multiple "phonemes" (cheremes?) happening at a time: different movements, hand positions, and facial gestures can all be happening at once. So figuring out how to serialize these languages is much more difficult. It can still be done—the most famous example is Sutton SignWriting—but it's significantly more complicated, since the language isn't already mostly serialized for you.
(*) The biggest exception being tone, in autosegmental theories. So you need to come up with a convention for this, like "write the tone for a syllable immediately after the syllable nucleus", which is what the IPA did.