I looked at this more last week. I suspect that NDSolve rather than parallel tools is the source of the problem (your ode results in something quite close to a step function. Quite challenging to solve!). I tried several different implementations using ParallelSubmit, ParallelEvaluate, and ParallelTable. Computation time sometimes showed speedup and sometimes not. I also tried v9 and v10 and saw no significant differences between the two.

I will ask some people more familiar with NDSolve to take a look.

I think per ParallelTable's doc page it should distribute the definition automatically because DistributedContexts -> Automatic is preset. Omitting d should not affect the performance.