"ELF" is a file format used for binary executable files in modern-day versions of Linux. ELF files for AIX cannot be expected to run under Linux anymore than Windows DLL files could be. AIX is not Linux, it's Unix, and Unix binary files are rarely that interchangeable even with other flavors of Unix.
Java programs would normally use the Oracle Type 4 JDBC driver. Type 4 drivers are 100% java, and therefore can be copied freely between machines regardless of what OS is in use. However, non-java programs require binary drivers, which cannot be copied freely, since they're not "Write Once/Run Anywhere" like Java is. The Oracle binary utilities such as SQL*PLUS are 100% OS-dependent, and you shouldn't even think about trying to copy them. Use the Oracle installer to install the appropriate client code for the OS that's going to be running it.
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