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As for factors that affect the rate of the Diels Alder reaction, having an s-cis conformation is primary.
But in a case as shown below, what makes the second diene react faster compared to the third?
The only reason I can think of is that the second diene has substituents pointing outward so they cause less steric hindrance as it reacts with a dienophile thus has a lower activation barrier. Are there any other underlying reasons apart from hindrance? 
You are correct that the having the diene in an s-cis conformation is extremely important. Only from this conformation can the Diels-Alder occur. If there is a high concentration of the s-cis conformer the Diels-Alder will likely occur rapidly; if there is a low concentration the reaction will occur more slowly.
In cyclopentadiene, the diene component has no choice, it is locked in an s-cis conformation by the ring. However with acyclic 1,3-dienes an equilibrium exists between the s-cis and s-trans conformations.
In 1,3-butadiene the amount of the s-cis conformation is relatively small (~2%) because of the steric interaction between the "internal" hydrogens at the ends of the chain in this conformation. In accord with this expectation, 1,3-butadiene is not as reactive as cyclopentadiene in the Diels-Alder reaction.
If we replace one of these "internal" hydrogens with a methyl group (penta-1,cis-3-diene), the steric interaction between the "internal" methyl and hydrogen in the s-cis conformation is even greater, further destabilizing the s-cis conformation and reducing the amount present at equilibrium. On the other hand, replacing one of the "exterior" hydrogens with a methyl group (penta-1,trans-3-diene) doesn't cause any increased steric interference in the s-cis conformation and the amount of the s-cis conformer is about the same as 1,3-butadiene. Again, in accord with expectations, penta-1,trans-3-diene reacts at a rate similar to 1,3-butadiene, whereas penta-1,cis-3-diene reacts slower.
Using this information we can make predictions for your compounds. We would expect cyclopentadiene to react the fastest because it is held in an s-cis conformation. In the case of cis, cis-2,4-hexadiene we now have an internal methyl-methyl interaction, which severely destabilizes the s-cis conformation, so there is very little present at equilibrium and this compound reacts the slowest in the Diels-Alder reaction. trans, trans-2,4-hexadiene only has an "internal" hydrogen-hydrogen interaction when in the s-cis conformation, therefore it should react about as fast as 1,3-butadiene - in between the extreme rates of the other two compounds.
It is indeed steric hindrance. It looks a lot less severe in the picture than it actually is. Remember that each end of the line is not just a carbon atom but a methyl group $\ce{CH3}$. That means that there are three further undrawn atoms bonded to the final atom of each side of the chain.
Now making the simplistic assumption that $\ce{C-H}$ bonds are similar in length to $\ce{C-C}$ bonds and just boldly drawing the hydrogens in a $120^\circ$ angle from those final carbons we notice that one hydrogen each would land on the carbon of the opposite end of the chain — very bad. If we twisted and turned a little, we could get around that, but all of the hydrogens would still be outstandingly close to each other. Therefore, (Z,Z)-hexa-2,4-diene will have a really hard time adopting the s-cis configuration.
The middle molecule, (E,E)-hexa-2,4-diene only has two hydrogens in the middle, which would hardly even notice each other.
