Subquaries in MySQL

"MySQL Server until version 4.0 only supports nested queries of the form INSERT ... SELECT ... and REPLACE ... SELECT .... "

in your case :
sql = "SELECT ID, Type, Name FROM Objects WHERE ParentID= (SELECT ObjectID FROM Permissions WHERE ObjectID=id AND UserID= (SELECT ID FROM Users WHERE UserName='userName' AND Password='password')) ORDER BY Type ASC";

I find this completely overkill and overcomplicated, at the limit of sophistication.

The first part could be written more simply as :
(1)

SELECT Objects.ID, Objects.Type, Objects.Name FROM Objects,Permissions WHERE Objects.ID=Permissions.ObjectID ORDER BY Objects.Type ASC;

think about what you try do get and incorporate your sub-sub-select ;-)

I guess something like this will do
SELECT Objects.ID, Objects.Type, Objects.Name FROM Objects,Permissions,Users WHERE Objects.ID=Permissions.ObjectID AND Permissions.UserID=Users.ID AND Users.userName='userName' AND Users.Password='password' ORDER BY Objects.Type ASC;

I recommend NOT trying to do this in a single query, but to make things clear and secure bu requesting the Users table first (identification), then only performing query (1)