How do 3 physically entangled particles work? Say a particle split into 3 particles that are all entangled to each other, if all 3 particles were to be measured simultaneously or rather if I'm to measure only one of them can I thus predict the quantum states of the other two? Imagine I used the other 2 pair for quantum teleporting 2 different states what is the answer for the last particle?
 A: 
"Say a particle split into 3 particles that are all entangled to each
  other, ... if I'm to measure only one of them can I thus predict the
  quantum states of the other two?"

Well it depends on how they are entangled. There are different ways in which three particles can be entangled. If we assume that somehow you've used the Kerr effect to split one photon into three, then they would be entangled due to the requirements for energy and momentum conservation. If you now measure say the momentum of one of the photons, then you can say something about the combined momentum of the other two, but it will still leave some variability that cannot be pinned down. So in general the answer would by: no you cannot in general predict the quantum states of the other two. However, they would still have some entanglement.

"Imagine I used the other 2 pair for quantum teleporting 2 different
  states what is the answer for the last particle?"

This question is not quite clear. If you want to teleport the combined quantum state of the remaining two photons with two seperate teleportation processes, what you would end up doing is soming called entanglement swapping. Whenever we teleport one photon that is entangled with another photon, we produce entanglement between the remaining photon and the remote photon. If we also teleport the remaining photon, we'll produce entanglement between two remote photons. 
If, on the other hand, you menat to use the two photons that remained after having measured the third to perform the teleportation of some given quantum states, then that can work provided that this pair of photons is properly entangled. If there is any restriction on the state that the two remaining photon can have, then that may restrict the kind of state that can be teleported.
Incidently, usually teleportation is used for qubits (two-dimensional Hilbert spaces). However, there is a way to teleport higher-dimensional states where the entangled states consist of more than two photons. See here.
