So playing teemo in nexus blitz gives you a big advantage, and that is you can cheat on events, how, just watch this. Play Video You get assist, you damage enemies and that in a event while you are forbidden to participe and you should be just a spectator (how i am while i play teemo support).
Also as teemo you have some advantages on battle royale events, if you are able to predict while the circle will be close (most of time is on a certain area) all you had to do is to go from start there, and place some shrooms, then just chill and wait, don't even look for your team. That work even better with paranoia battle royale while the vision on both teams is ****ed and you can freely even assasinate some low players with low chances to be observed.

So we talked about 3 events alerdy, hmm now what!?
URF, run along, place shrooms and stay invisible, but try to do spam some Q cause that mode is kinda r*tard and decide to reduce your hp if you don't suicide in enemies as fast as you can.
Teemo loot you need to follow the big teeto and hit him
Veigar loot you need to follow the little veigar and hit him and dodge his skills
The loot event is the best source of instant gold from that mode, abuse it as much as you can, and be sure both enemies and allies will stay away from that loot, just teemo deserve that gold.
Push the Cart basically stay afk in its range and look how it is moved itself
Scuttle Racing kill enemy crab and slow him to death
Sudden Death: Nexus Blitz last event of every match in nexus blitz, your nexus become some cool mecha and fight each other to decide which team will be victorious, the champions on both teams can attack enemies cool mecha nexus too.

So in that chapter i will try to cover the items that are exclusive for nexus blitz.
Depening on your playstyle there are few viable items for teemo.
First one and most popular probably is Stat-Stick of Stoicism this item is like half of teemo attack speed build, containing ap, attack speed and crtik chance, plus some other optionins, basically great for mix damage, and work good on any hybrid champion, but i don't recommand to rush it?! or do it, again is all up to you.

Sword of the Divine pretty good for attack speed teemo, its active grant you 100% crit for your 3 next hits.

Zephyr again good for attack speed/ad teemo, its passive basically grant you tenacity

Going on ap teemo build, there is Deathfire Grasp which grant 120 ap, cdr and his active target an enemy to deal 15% magic damage of his maximum health.

Spear of Shojin a tanky option, it don't grant to much, but would work in an ad build, or ad tanky build, still feel like i need to mention this item, cause of his passive, even tbh this item is for bruisers mainly