Murkrow's STAB Drill Peck is, undeniably, one of the best moves in a tier where Hitmonchan, Grass-types, and Bug-types abound. What's more, it's powerful enough to 2HKO 252 HP Piloswine and OHKO Raticate when boosted by a Choice Band, indicating its pure unadulterated power. Hidden Power Ground takes out the Rock- and Steel-types bold enough to try stepping into the path of Murkrow's Drill Peck, easily 2HKOing Sudowoodo, Lairon, Metang, and Graveler after a layer of Spikes. Hidden Power Ground is preferred to Hidden Power Fighting for its super effective hit on Poison-types, particularly Swalot, but Hidden Power Fighting offers a super effective hit on Normal-types and doesn't let the multitude of Ground-immune Pokemon switch in for free. Shadow Ball and Double-Edge are largely filler but can be used as safety moves when you're unsure of which way your opponent is going to go. Shadow Ball is particularly nice for its super effective hit on Chimecho and neutral hit on Rock-types.
A Jolly nature is absolutely needed to not only get the Speed tie with other Murkrow and Pidgeot but also outspeed the base 90 Speed tier, which notably includes Venomoth and Vigoroth. Dropping down to Adamant gives Murkrow more power, but losing those Speed ties and getting outsped by positive-natured base 80s like Glalie is a death wish. Sharp Beak can be used to bluff a Choice Band while keeping high power on Drill Peck and gaining the ability to switch moves, although the drop in power on its other moves is super noticeable. There are only two notable move changes to consider on this set. The first is replacing Hidden Power Ground or Hidden Power Fighting with Hidden Power Grass and using a Naughty nature, as doing so gives Murkrow an easy way to blow past its biggest nemesis in Relicanth along with Graveler and Whiscash. Hidden Power Ground will be better most times, however, particularly against the likes of Mawile and the other Steel-types. The second is Pursuit, which can be used effectively in the last moveslot over Double-Edge when you know your opponent is going to switch, in particular being a nice tool for Chimecho; just be sure to change Murkrow's nature to Naughty when doing so. Pursuit is a terrible move to be locked into, though, so it's recommended to only use it with Sharp Beak.
Spikes support is incredible with this set, as it pushes a ton of Pokemon into 2HKO range, particularly the Rock- and Steel-types weak to Hidden Power Ground, and the only Pokemon that can really tank attacks from Murkrow are grounded (Pelipper being about the only exception). Due to this, Glalie and Cacturne make exceptional offensive Spikes partners to use with Murkrow, and both have an easy time OHKOing the Rock-types that can withstand Murkrow's attacks.
Murkrow is a great counter to the defensive Grass-types in the tier and a great check to the offensive ones, meaning Rock- and Water-types such as Sudowoodo and Seadra appreciate having Murkrow as an offensive teammate to eliminate them. Murkrow also generally has an easy time with Chimecho, if it avoids Hidden Power Electric anyway, meaning Hitmonchan likes having Murkrow as a teammate too. Loading on Choice Band users on your team is a good strategy when using Murkrow, as very little in the tier can take on that kind of onslaught, particularly if Murkrow is used with its partner in crime Pidgeot.
Defensive Relicanth and Mawile are probably the best switch-ins to Murkrow, with the former only really fearing Hidden Power Grass and the latter weakening Murkrow with Intimidate. Due to this, Murkrow absolutely needs teammates that can reliably switch into these Pokemon and try to eliminate them. If your prediction is good, Diglett is an almost surefire way of trapping and getting rid of Mawile. Otherwise, a Grass-type like Tangela has a very easy time with Relicanth and other Rock-types, while Fire-types like Torkoal can switch into Mawile with impunity and force it out with Fire Blast. Plusle and Haunter have an easy time revenge killing Murkrow, so bringing something to absorb Electric attacks is a good idea; Grass- and Ground-types being good general partners to do so.