How do you deal with Ursa?

A few things can make Ursa's life very difficult.

First is to shut him down early with good disables

Ursa is pretty squishy early, and he can't contribute anything in a fight unless he can auto attack. Ursa needs Vladmir's Offering, Blink Dagger/Shadow Blade and Black King Bar before he can really contribute to fights other than running up to people his team chain stuns. If you can delay those items for a while, you can get items of your own to deal with him.

Speaking of items, Force Staff, Ghost Scepters, Eul's Scepter, Rod of Atos, Shiva's Guard, Heaven's Halberd, or enough armor from any source, all drastically drastically cut into Ursa's ability to quickly burst people down in the first few seconds of a fight. Assuming he was aware the fight was coming to preemptively cast the first overpower, he has 12 attacks in a fight before he becomes useless. True, that can be a LOT of damage, but if you get your teammates out of his way after the first 2-3 hits, he doesn't get the benefit of his fury swipes stacking up. He doesn't have the luxury of building good damage items, so without his fury swipe damage he isn't all that scary. That said, don't expect to win your first fight or 2 after he gets Black King Bar unless you have a good Black King Bar piercing disable.

Lastly, you can take the game late with counter pushers

Once your hard carry has a Butterfly/ Heaven's Halberd and Ursa's Black King Bar charges are mostly used up, he basically falls apart.

Venomancer

• Plague Ward are very good against heroes that naturally want to get Blink Dagger because if they catch you out at all and hit you, your Blink Dagger will be down for 3 sec and that can ruin an entire initiation
• Venomous Gale/Touch is very good because Ursa is kiteable

Disables

• Good against any carry really

Ghost Scepter

• He is primarily physical damage, so if he can't attack you, you're safe for a few seconds

Mobility

• Force Staff, etc.

High Armor

• Ursa is largely physical and usually doesn't build things like Desolator (can't right now anyway, you will be able to in 6.81) or Assault Cuirass, so high armor deflects a huge amount of his damage
• Shiva's Guard is particularly useful because it has an aura that provides attack/move slow, gives you lots of armor, and the active is another move slow

Kiting

• Ursa wants to man fight you, so just doing hit and runs, tempting him with different targets, etc. will allow you to run circles around him
• Ranged carries tend to work well

Attack Slows (semi-effective)

• These are good between bursts of Ursa's Overpower. He needs to hug a target and keep attacking them to build Fury Swipes. Heroes like Phoenix can shut him down.

Ancient Apparition

• Ursa is highly reliant on Vladmir's Offering during fights to keep at full HP. Ancient Apparition Ice Blast disables all healing, so he'll pop very fast.
• Ancient Apparition also has some minor slows

Stopping Rosh

• Watch Ursa's items when you get visibility of the hero --> he will Rosh soon after Vladmir's Offering is done
• A ward won't necessarily work near Rosh because h'll Smoke in, so just check it every now and then. Sometimes his allies give it away with odd movement around the map.
• Note the time Rosh dies so you can stop his next Rosh attempt. Even if he gets the 1st and 2nd Rosh, be sure to get the 3rd to deny his team access to Cheese.
• Pushing up mid and bot lanes can help so you have more vision of his side of the map. You may be able to catch him smoking up if the creeps are back far enough.

Team Fighting

Ursa thrives on pick-offs. In team fights, especially with coordinated disables or AoE, he gets rolled unless he has Io or someone to help him.