My elephant ears are around five years old. This year all three of them are producing at least 4 seed pods but no new leaves. Does this mean the plants are dying, and all the energy is going into making the pods? I plant them outside in the summer (zone 6) and bring them in over the winter.

No, not dying, they are not monocarpic plants. It's normal for them to slow or stop leaf production while they grow the seed pods.

If you don't want to grow out the seeds, just cut the spadix off