The [ ] is not part of the if-statement. if only requires a command (or a list of commands), not necessarily the [ ].
The [ ] is a command. It stands for 'test'
can also be written as if test $x...
The problem is that you use -a outside the brackets. The -a and -o operators belong to the test/[ ] command and can't be used outside. Then on the right side you use the || inside the brackets but...