These teams were both built with the knowledge that Duosion thrives after its teammates have removed problematic Ghosts / Psychics like Misdreavus and Grumpig that are able to Taunt Duosion out of setup, pokemon with Knock Off such as Simisage, Simipour, and to a lesser extent, Leafeon, and strong physical attackers (especially on team1, where Duosion is lacking Acid Armor) that are able to 2HKO Duosion like Mightyena, Dodrio, and Stoutland. Both teams seek to either gain momentum on these attackers in order to wear them down and force them out, or to remove them outright with their respective counters.
To start, I added Jumpluff as Duosion's primary partner on both teams. Given Jumpluff doesn't carry an item at all so that it can boost Acrobatics' damage, it takes Knock Offs for Duosion well and therefore preserves Duosion's Eviolite in that way. It also creates setup opportunities for Duosion through two means: firstly, Jumpluff lures out Zebstrika and Piloswine, both of which Duosion easily sets up on. Secondly, Jumpluff can put something to sleep and let Duosion setup on a sleeping Pokemon later in the match. Coincidentally, Jumpluff checks Simipour with Seed Bomb, Simisage with Acrobatics, Leafeon with Acrobatics, and Machoke lacking Ice Punch with Acrobatics, which again, helps Duosion keep its Eviolite. Finally, if you are using the version without Acid Armor, Jumpluff is easily able to outspeed and put heavy physical hitters like Mightyena and Stoutland to sleep before they threaten to 2HKO Duosion.
Next, I wanted a Fighting type that would also take Knock Offs and prevent Mightyena and Stoutland from beating Duosion, all while threatening out Misdreavus with the threat of either STAB Flare Blitz / Guts boosted Knock Off. Both Machoke and Monferno fit the bill here, given Adamant Monferno outspeeds Adamant Stoutland (and OHKO's Stoutland with CC if SR is in play) and can outspeed Mightyena's Sucker Punch with its own Mach Punch. Monferno however is less threatening to Misdreavus than Machoke is given Monferno does not pack something to hit Misdreavus SE with, so you have your options here (hence the two different directions of these teams).
Now that I had a Grass type, a Fighting type, and something that was very vulnerable to heavy physical hitters (especially with Dark type coverage), Dodrio was a huge threat that I had to account for. So, I added Probopass to the version with Machoke. It beats Dodrio that lack Salac Berry + Natural Gift, sets up SR for the team, and has excellent defensive synergy with its other 3 teammates: it protects Machoke from Flying / Psychic / Fairy, Duosion from Bug, and Jumpluff from Flying / Ice / Rock. In return, Jumpluff protects Probopass from Water / Fighting / Ground, with Duosion as a secondary Fighting resist.
I decided to take advantage of the slow Volt Switch that Probopass provides and to use it in tandem with Stoutland's great wall breaking abilities. Slow Pivot Probopass' Volt Switch essentially gives Stoutland more free switches for extra wall breaking opportunities, which made Stout an ideal partner. Jumpluff supports Stoutland by taking on the Fighting and Rock types that can sometimes give Stoutland trouble, and like Probopass, can give Stoutland free switches with its U-Turn if used with the appropriate timing. If you decide to use Swords Dance Jumpluff over U-Turn Jumpluff on Team1, Swords Dance variants of Jumpluff also greatly enjoy Stoutland's wall breaking.
And last, but not least, I noticed that I was fairly weak to Floatzel and other fast Pokemon because the team (outside of Jumpluff) was fairly slow as a whole at this point. At the same time, I did not have an Electric immunity in order to prevent my opponent from gaining momentum via Volt Switch (which is quite important to teambuilding down in PU). This is what prompted me to use LO Lightning Rod Zebstrika, as it solved both of these issues with the team.
Team 2 is very similar overall, but is a bit faster and therefore more offensive in nature. As it starts becoming different with Monferno over Machoke, I added bulky RP Relicanth as both a check to Dodrio and a temporary answer to Stoutland's CB Frustration. The Speed on its EV spread allows it to outspeed Zebstrika after a single Rock Polish, while maximizing Attack and using the remainder of its EVs for some mixed bulk. It does not take Stoutland's Superpowers well (68% chance to OHKO this Relicanth with CB Superpower after SR), but with Jumpluff and Duosion there, it is often unsafe to use Superpower against this team as it can end up with the opponent being crippled by Jumpluff or setup on by Duosion. With Relicanth being your answer to Dodrio, you're free to use a different Stealth Rocker like Piloswine, which also has an electric immunity, and therefore frees up your ability to use Sap Sipper on Zebstrika instead.
As a disclaimer (as Anty / GrimoireGod pointed out), the teams are weak to Floatzel, RP Regice (Team 1 especially), Scarf Simipour, and RD Golduck. You could possibly add Politoed or Roselia over Relicanth, but then that'd leave you susceptible to Dodrio + Stoutland. So, with that in mind, play carefully against these threats and enjoy the teams!