The only rectangle possible with this set is the 6x23 shown above. If we use one piece twice than we can form a 12x12 square. All 23 problems are possible.
Roel Huismann has found a number of simultaneous rectangles with the 40 one-sided tridominoes.
There are 211 tetradominoes including three with internal holes.
The 208 pieces without holes are shown here in eight 8x26 rectangles made by Roel Huismann and also in sixteen 8x13 rectangles made by Patrick Hamlyn. Patrick's solution can be coloured with just three colours.
We can also look at the solid tridominoes and form a number of three dimensional constructions the last of which shows a construction with eight internal holes.
One box is possible with this set a 2x3x23 as shown below.