I suggest that you build on a VM where you have sudo permissions. Then build libraries like OpenSSL using --prefix=/usr so that make install puts them in the usual system library.
Then build your tool, in this case Erlang, using -rpath. Then use ldd
to find all library dependencies for Erlang and any ports (C extensions) and copy those into Erlangs lib directory. Check all binaries and libraries with readelf -d to make sure that RPATH is set to $ORIGIN or $ORIGIN/../lib as needed. Use patchelf to fix these things if the linking process is not quite right (or you copied in secondary dependencies of system libraries).
Then use patchelf to set the interpreter for your binaries (not libraries) to point to ld-linux.so.2 in Erlang's lib directory. And then run a test suite using
strace -e open erl ...
to make sure that your build is not opening anything in /lib or /usr/lib.
At this point tar it up and it will run on any Linux.
See this question Compiling Python 2.6.6 and need for external packages wxPython, setuptools, etc... in Ubuntu for far more detail on how I built Python in this fashion.