[Overview]

Regenerator makes it a great Wish passer
Has awesome support options that few to no other Pokemon share in NU
Really bulky with good mixed defenses to take some neutral physical hits on top of special ones
Plays best on stall or on Trick Room teams with a dedicated Trick Room set
Inferior bulk to Lickilicky makes it a seem a bit outclassed, but Audino's perks over Lickilicky make it better for certain teams

[SET]
name: Cleric
move 1: Wish
move 2: Heal Bell
move 3: Protect / Toxic
move 4: Double Edge
item: Leftovers
ability: Regenerator
nature: Careful
evs: 252 HP / 4 Def / 252 SpD

[SET COMMENTS]

Allows Audino to play as a cleric, providing Heal Bell and Wish support for the entire team
Works best on bulkier teams or full stall teams that need Wish support from a specially bulky Pokemon
Wish to pass healing onto other teammates that may have no other form of recovery
Heal Bell to remove otherwise crippling status from itself and its teammates
While Audino can heal by switching, there are times it would rather stay in and heal from its own Wish; for these instances, Protect is preferred in the third slot
Toxic should be used if you are more worried about defensive Pokemon that can handle most of your team, though since many stall-based teams run Toxic Spikes, it may not be entirely necessary
Double Edge is used to keep Audino from being set-up bait, and it's chosen because the extra power is more important than the slight recoil which should rarely be doing much to Audino anyways thanks to its huge HP

[ADDITIONAL COMMENTS]

Audino's typing lends itself better to a specially defensive spread, since its Fighting-type weakness is a huge flaw for a physically defensive Pokemon
Thunder Wave
Plenty of other moves are viable over Double Edge; particularly special attacks, such as Flamethrower, Ice Beam, or Thunderbolt, though Double Edge does a better job of keeping Audino from becoming setup bait
Bulky setup sweepers love Audino's Heal Bell and Wish support, as an untimely burn or Toxic can cripple many of them and these moves give them a second chance to sweep: SubBU Braviary, Musharna without Heal Bell, Bulk Up Gurdurr are all good examples
Teammates that don't have any reliable recovery and hate status love the support Audino can provide: Skuntank, Metang, Regirock, etc.
Golurk shits on it outside of potentially being Toxic'd, and Mandibuzz, Alomomola, and Tangela all take it on well and work well as partners in general
Misdreavus also appreciates Heal Bell support since it often has no room to run it itself, and Misdreavus can take on most of the Fighting-types that threaten Audino

[Other Options]

Audino has a really cool movepool, filled with all kinds of potential moves it can use
Encore
Dual screens
Rain Dance/Sunny Day
Magic Coat
Yawn
Knock Off
Calm Mind set, but needs a lot of boosts to hit pretty hard
Has sick offensive moves, but it definitely does not have the offensive presence to use them

[Checks and Counters]

Taunt
Misdreavus in particular can Taunt and is immune to Double Edge and can recover loads of health back with Pain Split
Golurk only has to worry about Toxic and can fuck it up/recover with Drain Punch
Toxic Spikes; while it has Heal Bell, if you can get up Toxic Spikes against it, whenever it switches in, it will have to worry about using it in order to get rid of the poison
Really strong special attackers, especially with Focus Blast, can muscle past it: Charizard and Jynx are good examples of this
Fighting-types, especially Gurdurr and Throh since both benefit from status
Gothorita can trap it and set up Calm Mind against it, even beating Toxic variants of Audino thanks to Rest
You're often better off trying to handle whatever it switches out into, since alone, Audino is not very threatening; it's just the support it provides to its actually threatening teammates that can be a pain