How can I search molecules by constituent atoms
You can use ChemSpider's full search:

http://www.chemspider.com/FullSearch.aspx

and click on the 'Elements' section. Alternatively, there is a direct link here:

http://www.chemspider.com/ElementsSearch.aspx

This gives you two periodic tables that you can select elements from for your search. I think the upper one is 'allowed' and the lower one is 'forbidden', but I haven't tested this.

Of course, as pointed out in the comments, the set {C, H} will give you most of the database! However, for rarer elements this can be a better filter.