You don't say how much materials you are allowed to use of each one of the items you listed...I would say you basically make a crush proof container out of the paper and suspend the egg in the middle like your trying to send a piece of fragile glass across the united states without it breaking from all the bouncing,impacts it will suffer during the trip..you could roll sheets of paper into cylinders and then glue the paper so it will stay in the shape of cylinders and then use the cylinders to make a roll cage like a race car has to protect the driver(egg).then inside the roll cage you could wad up paper into balls and make a place(nesting place) for the egg to rest inside the cage suspended by the rubber band(shock absorber) in the middle of the cage..and the paper clip could be used as a stabilizer to help hold the nesting area in place like a seat belt inside the cage......