Going about it with a module is the right way. To answer your questions:
SCTP is already provided as a kernel module in the Linux source tree - "CONFIG_IP_SCTP=m" would enable that module. And you can change that to a "y" to hard link, though that is probably unfeasible, since you'd have to rebuild the entire kernel for that.
The module would have to still be built per kernel version. So basically per vendor, you'd need to get their kernel sources (doable), and then compile your module against it.
To use: In User mode - would create the socket by calling s = socket (AF_INET[6], SOCK_STREAM, IPPROTO_SCTP); From that point, socket APIs work exactly the same, with a few exceptions (namely setsockopt, which is particular for the protocol type).
From Java - does in fact support the protocol in its latest incarnations (JDK7 as of milestone 3), but that Java supports it doesn't mean that Dalvik (the "java vm" of Android) does. Though Android does have SCTP support "in the ready", it's not yet in Dalvik (at least not in 4.2). You could create a Java class, though, as in a package, that would wrap a native library with SCTP calls. It's a bit trickier in Android because of the NET permissions, but still manageable (from experience).
