"You have a strange hobby, which I do not really understand."
Translation:У вас дивне хобі, яке я не дуже розумію.
It's not a simple question to answer, but I will try. First of all, in my opinion, the english version of this Ukrainian sentence would be "Your hobby is strange...", not "You have a strange hobby". Hence, no need for the additional verb in both languages.
You can say "У вас Є дивне хобі...", and people will understand you, but it stresses slightly different thing.
"У вас дивне хобі" - In this sentence we want to emphasize the characteristic of the hobby, namely "strange" ("дивне"). - "Your hobby is strange"
"У вас Є дивне хобі" - in this sentence we are emphasizing the fact that the person HAS a strange hobby. - "You have a strange hobby" - In this case in Ukrainian it would sound odd, because you are telling to the person that he/she has strange hobby meaning that they don't know about it. But they do and you're just duplicating the info.
As a rule of thumb, if the fact that person has Y is known and you want to say some characteristic Z about the Y, you can omit "є". - "У вас Z Y"
"You have a nice car" - "У вас Є гарна машина" - you're telling a guy he's got a nice car in case he doesn't know (so it sounds odd as well, because if he's got a car, he probably knows it) "Your car is nice" - "У вас гарна машина"
On the contrary: "You have a beautiful daughter" - you can translate it both ways depending on the context. If, for example, a mother is sitting with her daughter somewhere and you tell it to her, you should tell "У вас прекрасна дочка", because she of course is aware that she has a daughter, so you emphasize her beauty, not the fact of her existing. If a dad, for example, doesn't know that he has a daughter and you want to give him that info and also to say that she's beautiful, you would want to use "Є" - "У вас Є прекрасна дочка"
Of course, it's not 100% rule, but in general it's correct.