Summer Elise

Boon: Atk or Spd (at +0, -Def is your best Bane)
Weapon: Gronnblade+
Support: Reposition / Draw Back
Special: Blazing Wind
Passive A: Heavy Blade 3
Passive B: Special Spiral 3 (effectively lowers Blazing Wind in this build to a 3-cooldown Special. This combined with Heavy Blade makes it incredibly easy to charge your Special.
Passive C: Odd or Even Atk Wave
Seal: Hardy Bearing
Summoner Support: Not necessary, but always welcome
Ally Support: Blue unit, preferably one who can deal with Red units with high Res, especially those that can still survive getting nuked by her and still counterattack.

Blazing Blade build with Heavy Blade and 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 as AoE Specials deal neutral damage). 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, 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). Special Spiral, if used correctly, is a much better alternative anyhow, letting her very easily charge her Special.
A movement-based Special will help her out greatly when she's on a team with at least 1 unit with a Link skill. Her C, being either of the Atk Wave skills, is immensely helpful for Gronnblade's damage output.

Paired with Elise's high attack and rather middling speed, Death Blow 4 and Gronnblade will be able to dish out a great amount of damage.
Draconic Aura gains an extra cooldown reduction, making it a 4-turn cooldown. She will usually proc Heavy Blade, and in 2 turns she will have Draconic Aura ready. For some odd reason, there was no option in the B slot for Special Spiral, but Special Spiral is the optimal B slot. If aiming to kill strong axes like Surtr and Hector, or Special Spiral is not an option, Axebreaker is acceptable, too.
Elise is a strong green mage that can be overlooked because of the others in her color. However, with the right buffs and the correct skills, she can be as strong as mages like Ophelia.

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.