When considering homework, the first point to understand is school policy. This means that you need to know what the policy is, and to know what it means. Often a policy is aspirational, it describes what the school wants to achieve; sometimes it is operational, and it describes what is really expected to happen on a day-to-day basis.
Regardless of what the policy is, you need to decide how you are going to put it into practice, and in terms of being efficient, the keyword is routine. You should establish a routine at the start of the year and keep to it. This means that the routine itself must be flexible enough to cater for your peak workloads.
You may wonder how you can have a routine and still be flexible, but there is no mystery about this. Tell your students at the start of the year that their homework will fall into different categories and tell them that there will be different levels of marking, including peer assessment; but also tell them that it will be handed out at the same time every week, that it must be handed in at the same time every week, and that it will be promptly marked and returned.
As far as possible, get the administration of homework - its distribution, collection, sanctioning, circulation of feedback - done by elves or other students; as far as possible, get it running like clockwork and keep it running like clockwork.
For a detailed example of how to use Elves in homework, click here.