Relic's attack slices through the kobold and sends it falling to the ground. (Scimitar Kobold 3: dead)

The undead bird, blocked by the presence of kobold, chomps at the bit where it stands.

Kobold 1, seeing yet another companion fall, disengages from the melee and begins heading down the Eastward tunnel.

 21, Raker (8 damage, movement reduced by 10ft)
20, Robed Kobold
17, Relic
8, Undead Bird
6, Kobold 1
4, Gaius <--------------- current
1, Robed Kobold 2

Gaius follows Raker to stand with Relic.  He looks to the left and sees the robed Kobold.  "I have something for you," he says to the kobold in Draconic.  With a smile he casts Witch Bolt at the robed kobold.

To Hit = 13

Damage = 5

Lightning arcs from Gaius to the kobold and it seems like it's going to be a hit. But just before contact is made the kobold reacts with a shield, turning the witch bolt's apparent hit into a miss. 

From the darkness two more sling rocks are lobbed from the East at the closest party member, Raker.

Rock 1
To-Hit: 10, miss

Rock 2
To-Hit: 8, miss

The Robed Kobold pulls out from his robes a piece of pork rind and waves his hands with an incantation to conjure a puddle of grease around the party. (Centering on the corner Southwest of Raker.)

(using log)
Raker Dex Save: 11+6 = 17, succeeds
Relic Dex Save: 1-1 = 0, fails
Gaius Dex Save: 5+2 = 7, fails

The conjured slippery surface catches Relic and Gaius off-guard, sending them prone however Raker is able to dextrously keep his footing as the initiative turns to him. After casting the spell he then begins trudging through the muddy terrain into back up the Northern tunnel.

Map Note: The green box/shading centered around the party is being used to indicate the Grease area of effect. I also deleted the shading for the dim/bright light while leaving the orange/yellow circles. (It was getting cluttered with all the shading.) 

21, Raker (movement reduced by 10ft) <--------------- current
20, Robed Kobold
17, Relic (prone)
8, Undead Bird
6, Kobold 1
4, Gaius (prone
1, Robed Kobold 2

Raker’s head turns around on a swivel, looking at the robed kobold to the north.  He heads north, through the rough ground, using a bonus action dash if necessary to reach the robed kobold, and attacks.  

Short sword : 10 to hit, for 10 points of piercing damage.  

Raker's blade is aimed true but before it hits its mark the kobold casts up another shield turning the hit into a miss. While shielded from the attack, you can see a look of terror come over the kobold's face.

From the darkness comes a draconic call of "Get of out there, Kashak!" and another Ray of Frost hurtling towards Gaius. (adv from unseen attack; disadv from Gaius be prone, normal attack)
To-Hit: 17
Gaius' base AC is 15, 17 from half-cover, so a hit
Damage: 6 cold

21, Raker
20, Robed Kobold
17, Relic (prone) <--------------- current
8, Undead Bird
6, Kobold 1
4, Gaius (prone, 6 cold damage, speed reduced by 10 ft)
1, Robed Kobold 2 (+5 AC for the moment from shield)

edit: grammar

Relic will use his movement to crawl out of the greased area and into the space directly up and right from him, then I think he has enough speed left to stand.

That done, he swings his axe at the creature in front of him.

Attack: 8, damage: 11

+ 6 on a critical (I'm on mobile which is why I'm typing this out by hand)

Yep. Enough movement for that.

As Relic crawls into the space the undead bird using its reaction (readied action: attack enemy that comes within 5ft of it) to attack the warforged.

To-Hit: max(12,7) //from prone advantage, but both are misses

Relic's axe swings to the bird but is unable to find purchase on the bird's bones.

The bird, now on its own turns, rears up for another attack.

To-Hit: 9, so miss

Kobold 1 takes the opportunity to dash into the darkness.

21, Raker
20, Robed Kobold
17, Relic
8, Undead Bird
6, Kobold 1
4, Gaius (prone, 6 cold damage, speed reduced by 10 ft) <--------------- current
1, Robed Kobold 2 (+5 AC for the moment from shield)

Gaius is chilled to the bone but manages to crawl north, heading for the square 15 feet from Raker.  He hopes to clear the effects of the Grease spell.

Quote from Mister_Whisker >>

Relic will use his movement to crawl out of the greased area and into the space directly up and right from him, then I think he has enough speed left to stand.

That done, he swings his axe at the creature in front of him.

Attack: 9, damage: 6

+ 7 on a critical (I'm on mobile which is why I'm typing this out by hand)

 quoting this for posterity so I remember what the result was (hovering over the 9 shows a roll of 11 without any modifiers being applied to the d20, despite it having been rolled as a 1d20+6, so I'm guessing there's a decent chance DDB will get wonky and alter the in-post result at a later point)

Gaius is able to crawl to the spot without issue.

Far in the distance a sound like stone grinding on stone can be heard for a moment.

Up by Raker the kobold extinguishes the hooded lantern with a quick incantation (prestidigitation) and then tries to make a run for it into the East.

So Raker can get an opportunity attack (with disadvantage due to darkness) on the kobold.

 map note: I uncovered another two squares in the Northeast. While technically not visible yet, the robed kobold by Raker retreating would be audibly-tracked via the sound of running so it made sense so that you'd be able to see where it was on the map)

21, Raker <--------------- current
20, Robed Kobold
17, Relic
8, Undead Bird
6, Kobold 1
4, Gaius (prone) 
1, Robed Kobold 2

edit: forgot to take off +5 AC from shield on Robed Kobold 2 now that it had its turn again

Opportunity attack (then will determine next step) : 

Raker sees his light go out and hears the kobold as it moves away from him.  He takes the opportunity to lunge and reach out in the dark with his short sword, hoping to stab him and bring him down as he is fleeing.  

Short sword (at disadv) : 12 to hit, for 8 points of piercing damage.  

The strike is a hit and deals a grievous wound to the kobold as tries to get away. It still stands but barely.

Robed Kobold 2: 8 damage

Raker moves 5 feet to the northeast and then another 5 feet to the east, then he tries to strike the robed kobold again, attempting to prevent him from getting away.  

(At disadv)

Short sword 1 : 17 to hit, for 6 points of piercing damage.  

Off hand short sword 2 : 9 to hit, for 3 points of damage.  

If the first hit drops the robed kobold, he will instead use his bonus action to dash, moving back to the south as far as he can, rejoining the others.

[[side note: With movement in the Variant: Playing on a Grid section there's a note about corners
 Diagonal movement can’t cross the corner of a wall, large tree, or other terrain feature that fills its space.
So the Northeast move, since it's across a corner, would be North (5ft) East (5ft) as opposed to just one Northeast (it's only the presence of a corner that makes the diagonal an issue in this case)
]]

Following the sound of its steps, Raker is able to catch up and strike at the robed kobold, sending it to the ground. (Robed Kobold 2: dead) After defeating it he heads back to the party.

[[with 30ft (due to rough terrain) used to get there, the cunning action dash brings him back to where he started]]

21, Raker
20, Robed Kobold
17, Relic <--------------- current
8, Undead Bird
6, Kobold 1
4, Gaius (prone) 

Relic takes a swing at the undead chicken, using booming blade to punish it if it attempts to escape.

Attack: 23 Damage: 7

+ 2 thunder damage if it moves

The blade is a heavy thrust but the undead chicken-bird is able to dodge it before it makes contact. It then attempts strike back but gets bamboozled as its beak meets nothing but air.

(To-Hit: nat-1)

21, Raker
17, Relic
8, Undead Bird
4, Gaius (prone) <--------------- current

Side note 1: at the moment feel free to go right after each other, bird is the only enemy close enough to affect things at the moment so no need to wait for other enemies' action right now

Side note 2: Attacking with range from the square Gaius is on to the Undead Bird seems like a 3/4 cover for the bird.

Gaius stands and draws a dagger.  He watches as Relic works to dispatch the foul fowl.  "What kind of idiot creates an undead chicken?" he quips to Raker.  "Relic, drop the stone and I will carry it."

Once the stone is dropped, Gaius casts Mage Hand to grab the Light stone and hold it aloft.

Raker moves to the south, sheathing his short swords as he goes.  If he can make it that far, he goes to the square immediately to the southwest of Gaius, where he dropped his short bow.  He bends down picking it up, and nocks an arrow, readying himself for next turn, looking to the east.  “An undead chicken?  What is going on in here….”

“Once Relic can dispatch that chicken we should keep moving.  Which way are you thinking?” He asks the other two.  “I’m thinking this passage to the north.  Raker kept that Sorceror from escaping so none are waiting that way.”

"We can figure that out once the chicken is returned to rest," Relic says.

Attack: 19 Damage: Unable to parse dice roll.

+ 7 Thunder damage from booming blade if the chicken moves

Gaius keeps watch down all four corridors while Relic fights the bird.