So basically, my mom recently remarried to a man with one daughter from a previous marriage. Obviously, she's my step-sister. Now, here's where I get confused; my step sister's mother had been married once before she met my step sister's dad and married him. In that first marriage, she had a son. When she had her second child (my step sister) in her second marriage (with my step dad), her two children were half siblings. My step dad is not my step sister's half brother's biological father. So, what do I call step sis's half brother, since he is technically family?
English has no name for a step-sister's half-brother but try drawing the relationships in diagrammatic form, rather then describing them in words. If English was interested in any relationship as distant as a step-sister's half-brother, wouldn’t your step-sister’s full brother be your step-brother? Then why wouldn’t her half brother be either your step-half-brother or your half-step-brother? If general English wanted to go that far, could you re-post the Question after seeking detailed answers from at least three or four WWWs specialising in genealogy.
Using the Online Oxford Dictionary definition 1.1
A person in one's wider extended family, to whom one is not closely related.
You could call him a cousin or cousin by marriage. But that would probably give the wrong impression, as cousin is usually used to mean 1st or 2nd cousin. Even the term cousin once removed meaning 'cousin of a different generation' is often misunderstood by the general population.
The best choice for general conversation would probably be 'step-brother' or, if you wanted to imply slightly more distance, 'sort of step-brother' although the latter would probably lead to a longer discussion than is normally required.