This is possible since GitHub introduced the advanced filters.
Show me all open issues that are labeled view/controller but are not labeled easy meat.
is:open is:issue label:"view/controller" -label:"easy meat"
Notice the - before label: which says do not give me the issues containing this label.
Show me all open issues that are labeled either major refactoring or needs thought.
This is not supported (using label:A label:B means A and B instead of A or B) but you can do two different queries:
is:open is:issue label:"major refactoring"
is:open is:issue label:"needs thought"
Show me every open issue that does not have any label.
Use the no:label query:
is:open is:issue no:label
As additional info, you can refer to the GitHub documentation. And, https://github.com/issues can be your playgroud–being authenticated, you can search all the issues from repositories you have read access!