Replacing strips between subfloor and underlayment
The short answer is that you can use almost anything solid with a few caveats:


Whatever you lay over it needs to be able to span any voids you leave. If you fill with solid plywood, that's not a concern. If you use something else as sleepers, your underlayment needs to be able to carry typical floor loads across the gaps. 
If you use sleepers and gaps, be aware of what's carrying them. Widely spaced sleepers with full-thickness subfloor over them, for example, should probably align with floor joists below. 
Everything should be glued and nailed (or, better, screwed). Use proper subfloor/construction adhesive. Take all necessary precautions to avoid creaks and squeaks. 
Fasteners need to be set flush or below. If you try screwing your selected material down and the screws strip out in the substrate and remain sticking up you have problems. 


I'll leave my answer intentionally vague as such because then you're free to source what's available and cost-effective.