I am running a health intervention among children. There are 6 clusters of neighborhoods that are included in our study,each with 48 households. The households are being measured on 7 key variables. 4 are ordinal measures,one is a continuous variable and 2 are binary.The assignment to treatment and control can happen only at the cluster level. I want to assign them to treatment and control that makes the two groups as similar as possible on all 7 key variables. Is using an euclidean distance measure between the two groups for all possible combinations the best way forward?
Euclidean distance would not be a good choice. Is a one-unit change in your continuous variable really the same as a 0/1 difference in one of your binary variables? What would happen if you scaled the continuous variable differently (e.g., income per week versus income per year)? And in terms of relation to health outcomes, does a 0/1 difference in one of your binary variables really have the same effect as a 0/1 difference in the other variable?
You need to apply your knowledge of the subject matter rather than depend on a rigid formula. Match as best as possible the particular variables that are best known to influence the health outcomes you care about. See how others in the field of health interventions have done such matching. Think about how you will explain your matching process when you write up your results for publication.