[siva]

I was wondering about Rohan's miltary set-up. I know Elfhelm and Erkenbrand were made joint Marshals but i'm having trouble finding out anything more.

Was Eomer Edoras' Marshal as well as being King?
How exactly was an eored etc of riders set up?
Is Eowyn being a shieldmaiden just a throw away line or is more known?

Help me please! I'm getting so hung up on details i'm not writing.

[Rhapsody]

There is a big deal on The Rohirrim military structure in, I thought, Unfinished Tales.

Here is a piece I found:
The king had under him various lords (for example, the Lord of Deeping Comb and the Lord of Harrowdale). The Marshals of the Mark were the king’s chief lieutenants; these three posts were filled by persons related to the king or by vassals. The evidence of Helm’s and Theoden’s reigns is that the king held councils, made up from his marshals and leading captains (LOTR Appendix A II, p.1103) but it is not clear if there were regular members and meetings. (See Unf tales "The Battles of the Fords of Isen", p.367-69 for details on Rohan’s military/power structure).

More googling:
Éoherë
Full muster of the Riders of Rohan. The eohere was the entire cavalry force. The size of the eohere varied over time. When Eorl rode from the North to the aid of Gondor in 2510, his eohere consisted of about 7,000 fully armed Riders and several hundred mounted archers.

Under the military reorganization in the time of King Folcwine, the eohere was determined to be composed of 100 companies. Each company - or eored - had at least 120 Riders. Thus at full strength the eohere of Rohan could number about 12,000 Riders.

During the War of the Ring, King Theoden said that he might have mustered 10,000 Riders to send to Gondor, but that some had to be left to guard Rohan's strongholds. The King led 6,000 Riders forth to wage war against the forces of Sauron at the Battle of the Pelennor Fields on March 15, 3019.

Other Names:
Also called the Full Muster of the Riders of the Mark or simply the Full Muster.

Etymology:
The word éoherë comes from the Old English eoh meaning "horse" and herë meaning "host, army."

Sources:
Unfinished Tales: "Cirion and Eorl," p. 298, 313 note 27, 315 note 36, 318-19 note 49

Éored
Company of Riders of Rohan. An eored was a group of trained warriors who rode as a unit. Under the military reorganization in the time of King Folcwine, the size of a full eored was determined to be at least 120 men. One eored was one hundreth of the eohere - the full muster of Rohan. The Riders of an eored could serve for a term or on a permanent basis. Each eored was led by a Captain. In times of war or unrest, the three Marshals of the Mark each had a battle-ready eored as part of his household which he could command at his discretion.

During the War of the Ring, Eomer, the Third Marshal of the Mark, defied orders and led his eored in pursuit of a band of Orcs who had entered Rohan from the Emyn Muil. In the battle between Eomer's men and the Orcs, fifteen Riders were killed. Eomer's eored thus numbered only 105 when they encountered Aragorn, Legolas, and Gimli on February 30, 3019.

Merry Brandybuck and Eowyn - disguised as a Rider named Dernhelm - rode with the eored commanded by Elfhelm to the Battle of the Pelennor Fields on March 15. When the Rohirrim charged onto the battlefield, Eomer led the first eored in the center while Elfhelm's eored was on the right flank and Grimbold's was on the left flank and the other companies followed behind. King Theoden rode before them all.

After the War of the Ring, Eomer returned to Minas Tirith with an eored of Rohan's fairest knights to escort the body of their slain King home for burial.

Etymology:
The word éored comes from the Old English eoh meaning "horse" and rád meaning "riding."

Sources:
Unfinished Tales: "Cirion and Eorl," p. 290, 301, 315 note 36; "The Battles of the Fords of Isen," p. 357, 362, 367-68
The Two Towers: "The Riders of Rohan," p. 32, 37, 39-40
The Return of the King: "The Ride of the Rohirrim," p. 104, 110-13; "Many Partings," p. 253

There is also a big chunk of information in The Lord of the Rings: weapons and warfare by Chris Smith

This is a direct copy and past from Unifinished Tales:

The King again took command in person, Éomer was reinstated, and became virtually first Marshal, ready to take command if the King fell or his strength failed; but the title was not used, and in the presence of the King in arms he could only advise and not issue orders. The part he actually played was thus much the same as that of Aragorn: a redoubtable champion among the champions of the King.*When the Full Muster was made in Harrowdale, and the "line of journey" and order of battle considered as far as possible determined, † Éomer remained in this position, riding with the King (as commander of the leading éored, the King's Company) and acting as his chief counsellor. Elfhelm became a Marshal of the Mark, leading the first éored of the Muster of the East-mark. Grimbold (not previously mentioned in the narrative) had the function, but not the title, of the Third Marshal, and commanded the Muster of the West-mark. † Grimbold fell in the Battle of the Pelennor Fields, and Elfhelm became the lieutenant of Éomer as King; he was left in command of all the Rohirrim in Gondor when Éomer went to the Black Gate, and he routed the hostile army that had invaded Anórien (The Return of the King V, end of chapter 9 and beginning of 10). He is named as one of the chief witnesses of Aragorn's coronation (ibid. VI 5).It is recorded that after Théoden's funeral, when Éomer reordered his realm, Erkenbrand was made Marshal of the West-mark, and Elfhelm Marshal of the East-mark, and these titles were maintained, instead of Second and Third Marshal, neither having precedence over the other. In time of war a special appointment was made to the office of Underking: its holder either ruled the realm in the King's absence with the army, or took command in the field if for any reason the King remained at home. In peace the office was only filled when the King because of sickness or old age deputed his authority; the holder was then naturally the Heir to the throne, if he was a man of sufficient age. But in war the Council was unwilling that an old King should send his Heir to battle beyond the realm unless he had at least one other son.(ii)A long note to the text (at the place where the differing views of the commanders on the importance of the Fords of Isen is discussed, (page 376-7) is given here.

Regarding Éowyn: she was the chosen leader of the Eorlingas while Théoden and Éomer were away helping Gondor in the Battle of Pelennor Fields. The title Shieldmaiden was given to her by Theoden.

Let me know if you need more.