Siobhan, why 3 values in 1 field? And what data type is the field? Finally, how to you intend to use the values later?
Given that you must then it's if (isset($_POST['oc6'])) { etc to get the checkboxes that were clicked.
Now the datatype of the db field will determine how you need to build the query string. If it is char then you just concatenate the value to the query string.
You could however use a bitmask approach. Your db field would be a tinyint and you would use the Bitwise operators to manipulate and query the stored values. Read the user notes on the manual page for functions that do what you need.