If Red is still alive after Bron's attack, Einar attempts to finish it off.

Attack: 26 with hatchet for 13 slashing damage.

If Red died to Bron's attack, Einar moves forward (to T7). 

(Will state the rest of his turn depending on what he sees.)

After the (red) goblin falls from Bron's attack, Einar moves east (to T7, using 20 feet). The cavern he enters is half filled with two large, basically empty pools. A narrow waterfall high in the eastern wall would feed the pools, after which, it would drain out the western end of the chamber to form the stream that flows out of the cave mouth below. Low fieldstone walls served as dams holding the water in. From the fact that holes have been knocked in the fieldstone walls and two large hammers have been discarded by the pools, Einar can deduce that the two floods were caused when the pools' walls were breached. A wide exit stands to the south, while one other smaller passage leads west. The sound of the waterfall echoes through the cavern, making it difficult to hear.

Nif will move to V11, drawing his shortsword and dagger. He will then attack blue goblin.

Shortsword Attack: 10 Damage: 4

Sneak attack bonus:6

Dagger: Attack: Attack: 21 Damage: 3

Seeing the path of the waterflow, Einar knows the path to his left leads back to the entrance, so he cautiously makes his way closer to the path into the large room, unaware because of all the noise from the waterfall that a scuffle has already begun.

Movement: As close as possible to the goblin chamber. I thought I only used 15ft to get to T7, but I'll go with the DM's ruling.

Nif stealthily slides along the wall behind the (blue) goblin. He draws his shortsword and dagger and attacks. The shortsword slices down the back of the (blue) goblin, catching him by surprise and cutting a little deeper than it would otherwise. The goblin bends forward and Nif's second attack catches only air. The (blue) goblin is still on its feet, though looking rough. The (green) goblin immediately reacts to his compatriot's cry and rushes toward Nif (V12) and swings his scimitar. (Attack: 6) Nif sees the second goblin rushing him and is able to duck out of the way of the attack.

Back north, Einar jumps over the mound of three dead goblins and travels east, through the pools cavern, and up the stairs to the south.

(Yeah, I was already figuring the rage was going to end once Bron's attack finshed off Red. Further, Einar knows nothing of what's happening up the stairs because of all the noise you mentioned from the waterfall. As such, he has no narrative reason to dash forward. He is wary of further traps. Thanks for clarifying about the difficult terrain, though. That slipped my mind.)

Karl moves to U13 to close in on Green Goblin. With a mighty swing of The Rattle he pounds its head down into its torso, 

Karl steps out of the darkness of the back of the cavern and surprises the (green) goblin with a mighty whack to the back of its skull. The crack of splintering bone echoes off the walls.

After smashing in the Green Goblin's head Karl moves onto U12.

Karl moves north five feet (U12). The wolf, in response to the (blue) goblin's cry, jumps to its feet and runs up (W11) and attacks Nif. (Attack: 5, Fumble: 7) The wolf attacks with such exuberance that it misses Nif and almost loses its footing, but having four legs instead of two keeps it on its feet.

Vondal grimaces at the sheer number of goblin bodies, but presses forward till he can peek around the corner. Seeing no sign of Nif and Karl coming around the bend, he glances once back at Bron with a questioning look, and then says to Einar in what he originally planned to be a whisper, but has to be quite a bit louder to be heard over the sound of ... is that a waterfall? "Where are our brothers?" He creeps eastward, seeing in fact the waterfall in the east, and then squeezing by Einar and hiding behind a stalactite (U8).

The bugbear beared its teeth as Nif and Karl appeared. As the wolf tore around him to attack Nif, the bugbear moves around the campfire toward Karl. "Klarg glad you came. Klarg will build a throne from your bones, puny ones!" He swings his morningstar upward at Karl (Attack: 24, Damage: 12), catching the dwarf in the chin and knocking his head backward. Karl collapses, and the bugbear turns its eyes on Nif and moves closer (U11).

Retcon: The wolf, in response to the (blue) goblin's cry, jumps to its feet and runs up (W11) and attacks Nif (rolls in spoiler above). Thanks to the (blue) goblin's distracting of Nif, the wolf is able to get under Nif's defenses, grabbing hold of his leg and knocking Nif to the ground, tearing a chunk out of the dwarf's leg in the process.

Karl's death save 4

Bron Dashes down the passage, following the others towards the sounds of fighting.

Bron dashes east across the bridge, navigating through the pile of goblin bodies, through the cavern with the waterfall, up the stairs, and gets as far as the entrance to the southeast cavern (X11) where a wolf, a goblin and a bugbear are surrounding Nif, who is on the ground and bleeding from the leg. Karl and a second goblin are lying motionless on the floor, either dead or unconscious. The (blue) goblin turns and brings his scimitar down upon Nif (Attack: 18, Damage: 5) Nif groans and then falls silent. The wolf, goblin and bugbear turn to look at Bron.

Einar rushes after Bron. As he climbs the stairs and spots the enemies surrounding his fallen brothers, he lets out a howl and hurls his hatchet at the nearest Goblin.

Movement: To X10

Action: Attack 13 with thrown handaxe, targeting Blue Goblin for 10 slashing damage.

Death save: 3