Summer Elise

Probably the most effective but expensive build for Summer!Elise I can think of building.
Gronnblade+ has synergy with Glimmer, Even Spd Wave, and Heavy Blade; Glimmer has synergy with Atk/Spd Push and Heavy Blade; and Atk/Spd Push has synergy with Even Spd Wave, Renewal, and Heavy Blade.
Even Spd Wave, regardless of having an adjacent ally, gives the unit +6 Spd for one turn every other turn, which just so happens to affect Blade tomes for more damage during those turns. Gronnblade+'s effect of getting more damage from Even Spd Wave, as well as Atk/Spd Push adding more Atk and doubling potential while at full HP, increases the damage you get when activating Glimmer. Though Gronnblade+ does turn Glimmer into a 3-charge Special, Heavy Blade helps (with a higher likelihood thanks to Atk/Spd Push) to charge it in two attacks and activate it in the third.
Renewal is there to help get Summer!Elise back to full HP so she can proc Atk/Spd Push more often. Still, she should have someone that can heal her to full — whether it be a healer or pseudo-healer — and having an HP bane greatly increases the number of units that can do this with Reciprocal Aid. Her default Rally Atk/Res is good to stay, though you could perhaps give her Harsh Command as the meta is starting to use debuffing skills more than ever. A positioning skill like Draw Back or Reposition would also be wise, especially if you happen to have an Armored ally(s).
An Atk boon is best because you're already getting enough Spd from Atk/Spd Push and Even Spd Wave, and you want to maximize the damage you can deal with Gronnblade+ and Glimmer.
For her weaknesses...give her Hardin, Lance!Lucina or Shiro as her ally. They're plenty tanky and can deal with most Red threats, especially if the latter two inherit Berkut's Lance+. You should also give her a Dancer as an ally, like Performing!Azura or Performing!Olivia; Performing!Shigure would also be welcome with his Geyser Dance, but if you use both a Lance user and Performing!Shigure your last unit will likely HAVE to be Red to balance out the team. As your Red ally, Default!Eirika would be the best (especially because of her Sieglinde's Hone Atk 3 effect, as well as its unique Forge refine effect).

Merged +1

Originally opened a -att +spd that broke my heart because I didn't want to use her with a -att bane and it took 6 summer Xander's to finally get her last day. Opened this one during the legendary banner she was on by accident since I wasn't opening for greens to begin with but when I saw +spd and not -att I was so happy.

Decided to go for the glass cannon build since I love seeing high attack values.

Draw back is my current choice for safety reasons but if I decide to use her in arena I might swap to rally att/res from her base kit for more scoring.

Summer Owl:
IV's: +Spd -Hp
A standard owl tome build for anyone who already has a dedicated Gronblade user, Elise has the same attack and three more points of speed when compared to Mae, making her a slightly stronger but frailer version of her.

A speed refinery should be taken to boost Elise to a crisp 42 speed and 50 attack when combined with Fury. Desperation is self-explanatory. Her assist and C skill are flexible, if she feels too frail go with Ardent Sacrifice to safely put her in Desperation range, if she seems fast enough then change Threaten Speed to whatever is desired. It's worth noting that Elise probably isn't the best unit to run ploy skills thanks to her good but not great Resistance stat.

Boon/Bane: +Atk/-Def or +Spd/-Def
Weapon: Gronnblade+
Support: Rally Atk/Spd / Draw Back
Special: Blazing Wind
Passive A: Heavy Blade 3
Passive B: Desperation 3 if not equipped with Hardy Bearing Seal; otherwise Versatile. I picked G Tomebreaker 3 to help against Nino, but Lancebreaker 3 is a good alternative if you're afraid of Camus
Passive C: Versatile, preferably Hone/Spur/Drive or Threaten skill.
Seal: Hardy Bearing 3
Summoner Support: Not necessary, but it's always welcome
Ally Support: Blue Tome or Lance. Preferably someone who can deal with Red units, especially those that can still survive getting nuked by her and still counterattack (like Xander or Celica).

Heavy Blazing Blade build with Hardy Bearing. This build turns Summer!Elise into a nightmare for any non-Red without high Res (and even then, some mid-Res Reds fall victim). Gronnblade's effect with Blazing Wind and Heavy Blade combine into a quickly-charging nuke that benefits from Hone and Fortify buffs and destroys group-reliant teams.
The Hardy Bearing Seal will be your best friend here. One of the most glaring weaknesses of all of the AoE nuke Specials is that they essentially help your opponent set up Vantage for free; with Hardy Bearing you won't have to worry about taking damage before you attack. It does prevent you from using Desperation's effect, but it's a small price to pay when you do so much damage (especially when you consider that you're already doing two uninterrupted amounts of damage, so you're technically getting Desperation anyhow). I personally went with G Tomebreaker to help against Green Mages like Nino who are fast enough that she has trouble doubling them a lot of the time.

EDIT: While this build is still mostly-viable...well, let's just say that everything that's happened between her creation and now has not done any favors for her at all. Even though her natural weapon, Hibiscus Tome+, got a Weapon Refinement...it got probably THE worst treatment out of everything (with no effect boost and only minimal flat stat increase options). Though this build doesn't care about her natural weapon, Gronnblade+ also hasn't received any upgrades...add that to all the Bonus Negation (especially the inheritable weapons from the Love Abounds banner) and you're looking at what's probably a dead build.
See, and you wonder why Fire Emblem almost faded into obscurity before Awakening came along...

-Death Blow 3 and Gronnblade+ Combo to deal slightly more demage(Boosting her ATK stat to 56 at this point), eventually one-shooting units low on RES(even Sword-Units)
-B Tomebreaker 3 to gurantee doubles against blue mages because of her superior RES(also to improve her as a Reinhardt-Counter)
-G Tome Valor 3 for making it easier to gain SP for her and other green mages
-HP+3 Seal to increase her chance for survival