I am calling gcc through PHP by means of exec command. Then gcc gives weird errors such as "stddef.h cannot be found".

PHP is running under username "oracle". That is, when we call "whoami" through a PHP script by means of "exec", it gives oracle as the username.

We can easily call gcc without error on the terminal.

We can call "sudo -u oracle gcc source.c" without any error.

So it is very weird to me. Any ideas???

gcc should not be still installed on a server ( unless setting it up ) and most defiantly should not be accessible through a web interface PHP cgi script .

you should be using ssh on a remote login

now seeing as this is Red Hat have you searched the RHN knowledge base ?
https://access.redhat.com/knowledge/search
you will need to login to your RHN account to access the docs

my friend if you don't have any idea why are you answering? Whats the point? And "should not" is none of your business. May be I SHOULD. How do you know may be it is really necessary.

there is still on useful information
( assuming that RHEL's default Apache is used to serve up the *.php pages )
Is this a Oracle "unbreakable Linux " or is it RHEL 5 or 6 running a Oracle DB
both Oracle and red hat are not free you must have a paid for support contract

also
having the default DB user "Oracle" be able to BUILD software from a web interface ( can you say SQL injection ) is not good idea

Have you set Apache to allow cgi ?
have you set up the server TO allow that user to access the OS root dir "/" ( never a good idea)