from question we can conclude that ...
L1<L2
L3<L2<L4
now take first statement
I. if L4 belongs P, then L2 belongs P this is true because L2 is polynomial time reducible to language L4
II. if L1 belongs P or L3 belongs P, then L2 belongs P not possible because L1, L3 is is polynomial time reducible to language L2, not L2 is polynomial time reducible to language L1,L2.
III. L1 belongs P, if and only if L3 belongs P this is not true because looking at L3 we can not define L1 or simply we can say that L1 is not polynomial time reducible to language L3
IV. if L4 belongs P, then L1 belongs P and L3 belongs P this is true because we know that L1<L2 & L3<L2 and L2 is polynomial time reducible to language L4 so we can say L1&L2 also be polynomial time reducible to language L4.
So option C is correct.