function to sanitize input to Mysql database

Magic quotes are deprecated. Turn them off if you can :).

The second part addslashes and mysql_real_escape_String does pretty much the same (similar) thing. Just try

addslashes( '\\')
// and
mysql_real_escape_string( '\\')

Result should be \\ so if you use

 mysql_real_escape_string( addslashes( '\\'))

you should get \\ (or '\\\\' as string). Use only mysql_real_escape_string (better) OR addslashes, never both.

I recommend to use PDO instead of raw functions and manual escaping.

htmlentities() is unnecessary to make data safe for SQL. It's used when echoing data values to HTML output, to avoid XSS vulnerabilities. That's also an important security issue you need to be mindful of, but it's not related to SQL.

addslashes() is redundant with mysql_real_escape_string. You'll end up with literal backslashes in your strings in the database.

Don't use magic quotes. This feature has been deprecated for many years. Don't deploy PHP code to an environment where magic quotes is enabled. If it's enabled, turn it off. If it's a hosted environment and they won't turn off magic quotes, get a new hosting provider.

Don't use ext/mysql. It doesn't support query parameters, transactions, or OO usage.

Update: ext/mysql was deprecated in PHP 5.5.0 (2013-06-20), and removed in PHP 7.0.0 (2015-12-03). You really can't use it.

Use PDO, and make your queries safer by using prepared queries.

For more details about writing safe SQL, read my presentation SQL Injection Myths and Fallacies.