Elements of the style
Wesnoth is a game of heroic and high fantasy. In writing for it, you should use formal and poetic language with enough archaic words in it to convey a feeling of grandeur and times past.
In English, there is no need to go all the way back to the Elizabethan english of Shakespeare, but you do in general want to sound like a fantasy novelist of Victorian or Edwardian times. J.R.R. Tolkien was, of course, the best known of these; other good models are Lord Dunsany, E.R. Eddison, or James Branch Cabell.
Beware of sounding like a bad parody, however. When writing in this style it is easy to become florid and overwrought. Restraint is important, otherwise readers will just laugh.
If you are a good writer and very sure of yourself, you can mix in some elements of modern 'street' language, especially for comic and intimate scenes and when you are doing irony. But try not to mix mall-rat slang and archaisms in the same dialogue, the effect is too jarring. See "The Rise of Wesnoth" for a campaign in which occasional modern intrusions in the fantasy-poetic language are done well and transitions from one to the other are particularly smooth.
Use the forms "elves", "elven", "elvish", "dwarves", "dwarven", and "dwarvish", rather than the older spellings using 'f'. Mainstream English is tending this way anyway under Tolkien's influence and they are now definitely preferred for fantasy use.
In English it is legitimate to either treat all names of speaking peoples as proper nouns to be capitalized (Humans, Elves, Dwarves, Orcs) or as common collective nouns not capitalized (humans, elves, dwarves, orcs); howver these two conventions should not be mixed in the same work. In BfW we use the second convention.
Be careful about plurals and possessives and don't misplace apostrophes. Note that "lich", like other English words ending in "ch", pluralizes as "liches", not "lichs".
When referring to a specific unit type (e.g. "Spearman", "Ulfserker", capitalize it when talking about the unit in the narrator's voice, but do not do so when characters are speaking. Thus, the narrator might say "You may now recruit Spearmen", but a character would say "We should send some spearmen to protect the eastern gate."
Dialogue and accents
In general, formality and elaboration of speech should increase with social rank. (This is true in every society, but strongly true in the European medieval societies that are the models for Wesnoth.)
Magic-users and liches (especially high-ranking ones) should sound like nobles. (They have to be educated and literate.)
Dwarves have been given the accent of old-time highland Scots. When translating into other languages, pick an accent associated with tough, stubborn mountain folk.
Ogres and trolls have crude and rather mangled grammar. This is deliberate, as they are rather stupid by human standards.
Orcs and goblins, which are a bit brighter, should speak mostly correct but rather crude and vulgar language. Notice the epithets they have for other speaking peoples ("tree-shagger", etc.) and use them freely; they are a window into how orcs think.
Elves should have the most refined, correct, and elaborate speech. Common elves should sound like human nobles, and noble elves like human orators and poets.