Overpower (W): This is the big money right here. This gives Ursa maxed-out attack speed for 3/4/5/6 attacks depending on level. It wears off after fifteen seconds and has a cooldown of ten (you can't have it activated more than once, though). Definitely Ursa's bread and butter, and a big reason why attack speed/agility items aren't a big deal for him.
Fury Swipes (passive): Causes consecutive attacks to deal more damage to the target for fifteen seconds (or 6 seconds for Roshan). This used to be a unique attack modifier, and then Valve changed it because why not let him carry Desolator and fuck people up even worse?
Ursa is made mostly to take on Roshan, a super-powered neutral creep that coughs up an item called the Aegis of the Immortal whenever it dies. It's an item that revives you once you're killed, functionally doubling the length of Ursa's life and enabling him to survive big teamfights better, whether that means to run away or to tear up the entire team. As a result, Ursa is generally built in exactly one way: max out his passive by level 7, have Vladimir's Offering by then, then go beat up Roshan at your earliest convenience using the bonus gold to piggyback onto items to help you chase heroes, then beat people up until your Aegis is broken, then get ready for the next Roshan fight. As such, it should be quite clear what his weakness is -- if the opposing team has even the vaguest skill in denying creeps, Ursa is going to be losing out on a lot of gold. Thus, laning against Lich, or an Enigma who's smart enough to turn his own creeps into Eidolons, is a horrendously bad time for Ursa.
Ursa is extremely easy to "call," too. If the opposing team has an Ursa, he is probably playing to that exact strategy. Cutting off his farm and generally making it so he must fight Roshan later -- thus making it harder for him to do so, as Roshan gets harder as the round goes -- is something that can and will happen in any round against Ursa. There aren't really that many ways around it, but you can play Ursa as a jungler to help make things less of a pain for yourself. The easiest way to do this is by doubling up on Overpower. Basically, you use Overpower once, then wait for it to go off cooldown, use up all its attacks, and activate it again. With the addition of a liberal helping of Fury Swipes, you can wreck higher-level neutrals earlier in the game. Add Vlad's, and beating up the highest-level neutrals becomes a handy way to get some quick cash if you have nothing else you're doing (probably a pretty rare occurrence, to be fair).
I'll give Ursa a passing grade even if he is a complete monomaniac from a strategy perspective. I like him.
