This set is the best way to take advantage of Vespiquen's above-average bulk, Pressure ability, and reliable recovery. Vespiquen can switch in on a resisted Choice attack such as Earthquake, Close Combat, or Leaf Storm, forcing the opponent to switch out and giving Vespiquen the opportunity to set up a Substitute. Behind a Substitute, Vespiquen is protected from status and super effective attacks such as Stone Edge and Fire Blast, which she is able to stall out of PP by repeatedly using Substitute to abuse Pressure. If the opposing Pokemon lacks such dangerous moves, Vespiquen can hit it with Toxic and proceed to stall it out with Substitute and Roost. Slow, bulky Water-types that Vespiquen outspeeds, such as Slowbro and Quagsire, are easily defeated with this strategy if they lack Rest. Finally, Vespiquen can use her signature move, Attack Order, to counter certain frail special sweepers. Life Orb Alakazam and Choice Specs Sceptile are both OHKOed, and neither one can 2HKO Vespiquen with any of their standard attacks.
The given EVs maximize Vespiquen's special bulk, allowing her to repeatedly switch in on special attackers who lack powerful super effective moves. HP is not maximized to prevent Vespiquen from fainting on the second switch into Stealth Rock, although Rapid Spin support is highly recommended when using Vespiquen as it will make keeping her healthy significantly easier. The remaining EVs are placed in Defense to slightly reduce the damage taken from resisted physical attacks Vespiquen may switch into.
Poison- and Steel-types are immune to Toxic and resist Attack Order, meaning they can just about switch into this set for free. Aggron, Toxicroak, and Drapion will all gladly come in on any move and set up while Vespiquen is forced to switch out. To discourage this, Vespiquen could run Hidden Power Ground over one of her other moves. Even with a hindering nature and no EV investment, Aggron will be easily 2HKOed and Toxicroak and Drapion are both 3HKOed, which is enough to limit a sweep and prevent further set-up if Vespiquen hits them as they switch in.
An easier solution is to provide Vespiquen with a Ground-type teammate who can smash Poison- and Steel-types with STAB Earthquake. Donphan can check Aggron, Toxicroak, and Drapion very well, and also provides Rapid Spin support to prevent Vespiquen from losing half of her HP each time she switches in. Vespiquen and Donphan also have good defensive synergy, as Donphan can tank Flare Blitz and Stone Edge all day, while Vespiquen can easily switch in on Leaf Storm aimed at Donphan. Hitmontop is another reliable spinning partner for Vespiquen. He resists Rock, has solid physical defense alongside Intimidate, and can hit Steel-types hard with Close Combat. He also appreciates Vespiquen's ability to take on Psychic-types such as Alakazam and Slowbro.
Though not a necessity, having Toxic Spikes support would allow Vespiquen to drop Toxic from her moveset, making room for another move such as Hidden Power Ground or Defend Order. Nidoqueen and Drapion are both solid choices to provide this, but Nidoqueen has the bonus of being able to hit many of Vespiquen's counters hard with Earth Power or Ice Beam. For offensive teams, Vespiquen's biggest contribution will be eliminating Slowbro or Quagsire, so Pokemon who appreciate their removal are good partners. Kabutops and Blaziken can easily power through a team once the opposing bulky Water is defeated, making them both excellent partners.