Okay, so let's start with oligomycin. Oligomycin is an inhibitor of ATP synthase. So if you know how ATP synthase works, it's driven by a proton "channel" (more like a proton wheel) that spins and that twisting force is conveyed up a rod that also turns and forces ATP molecules out at the active site. Remember that ATP synthesis is not the RDS for ATP synthase - rather, it's the release of ATP that requires the energy. So oligomycin is an inhibitor that blocks the proton channel, which then stops oxidative phosphorylation and respiration because there's no way to dissipate the proton gradient that builds up so at some point, Complexes I, III, and IV can no longer pump against the huge proton gradient. And since ATP synthase isn't turning, there's no ATP and the cell starves for energy.
DNP, or dinitrophenol, is an uncoupler. What it does is it uncouples proton transport from oxidative phosphorylation. That's a fancy way for saying it shuttles protons across the membrane so that the proton gradient can be dissipated. Think of it as punching holes in the inner membrane if it makes it easier for you. It's called an uncoupler because it uncouples proton transport from ATP synthesis. So complexes I, III, and IV can resume pumping protons across the membrane and the DNP will keep shuttling it back across, helping to dissipate the proton gradient so the complexes can stay active. Therefore, O2 will be consumed to do this. However, no ATP will be produced.