If they are part of the same logical argument, then they are contradictory. Any argument that includes both of these statements will be an invalid argument.
Details:
The first statement says "either (H and J) or (N and J), or both, are true"
while the 2nd statement says "If (N or H) are true, then J is false."
Therefore, the two statements can not be simultaneously true.
Below is a conditional logic proof to illustrate.
1. (H • J) v (N • J) Premise
2. (N v H) --> ~J Premise
3.:: H Conditional Proof (CP) assumption #1
4.:: J CP assumption #2
5.:: (H • J) 3,4, Conjunction (CONJ)
6.:: (H • J) v (N • J) 5, Addition (ADD)
7.:: H v N 3, ADD
8.:: N v H 7, Commutation
9.:: ~J 8,2, Modus Ponens (MP)
10.:: J • ~J 4,9 CONJ
11. J • ~J 3-10, CP
Line 11 shows "J and not J" follows from the two premises, and this is a contradiction.
EDIT: 1) Fixed line 10 to read '4,9 CONJ' (was '4,10 CONJ') and adding this
note: 2) Lines 5 & 6 are not strictly required, but included to show the CP assumptions lead to the first premise being true.
