Elmers wood glue will work just fine. I did some tests and the mdf broke before the glue joint did. This was 2 pieces (1 flat, 1 length wise) and I did not clamp it. Once the box is built the box will strengthen it's self as a structure. MDF will slit easily if you try to screw too deep lengthwise (nothing rude meant here). I did some screw tests and found that if you pre drill (with countersink for asthetics), put a drop of wood glue in the hole, then add your screw, that sucker is not going anywhere. The glue around the screw and MDF strengthens that spot, therefore less chance for splitting ot stripping later. It is permanant though. Wood glue and clamp your wood joints.