My auto-siphon clogged so I had to transfer my wort to the carboy with a funnel. Some of the whole hops came along for the ride. I wouldn't mind but I was planning on pitching my barleywine onto the yeast cake. I'm not sure what to do,
The beer fermenting is an IPA. I was going to let it go a week and then rack to dry hop. Should I try to strain out the hops (after racking the beer) with a funnel and screen? How about racking the beer, pitch onto everything, and rack the barleywine once fermentation is active?

I would just move to secondary when you are ready and wash the yeast. that will keep the hops out and give you lots of yeast. wash it and use all of it, don't divided it out. you could even wash and make a starter to have even more!!

Do you think I'll need to strain the hops out with the screen/funnel?

nah, it should settle out to the lowest level when you wash it. I dont see that it would hurt though and I guess just pouring out all the trub, adding a bit of water and filtering it would work, washing may not be needed.

Put a nylon sack or something over the end of your autosiphon as a filter when you transfer. Then wash the yeast cake and you should be good to go!