I am looking for battle speeches like the one Théoden gave prior to the Battle of the Pelennor Fields in The Return of the King:
Arise! Arise, riders of Théoden! Spears shall be shaken, shields shall be splintered! A sword-day, a red day... ere the Sun rises! Ride now! Ride now! Ride! Ride to ruin... and the world's ending! Death! Death! DEATH! FORTH EORLINGAS!
Not sure if these count or not:
Fingon before the Nirnaeth Arnoediad
Then when Fingon heard afar the great trumpet of Turgon his brother, the shadow passed and his heart was uplifted, and he shouted aloud: 'Utúlie'n aurë! Aiya Eldalië ar Atanatári, utúlie'n aurë! The day has come! Behold, people of the Eldar and Fathers of Men, the day has come!' And all those who heard his great voice echo in the hills answered crying: 'Auta i lómë! The night is passing!'
The Silmarillion - Chapter 20 "Nirnaeth Arnoediad"
Fëanor before the Flight of the Noldor
Fëanor was a master of words, and his tongue had great power over hearts when he would use it; and that night he made a speech before the Noldor which they ever remembered. Fierce and few were his words, and filled with anger and pride; and hearing them the Noldor were stirred to madness. His wrath and his hate were given most to Morgoth, and yet well nigh all that he said came from the very lies of Morgoth himself; but he was distraught with grief for the slaying of his father, and with anguish for the rape of the Silmarils. He claimed now the kingship of all the Noldor, since Finwë was dead, and he scorned the decrees of the Valar.
'Why, O people of the Noldor,' he cried, 'why should we longer serve the jealous Valar, who cannot keep us nor even their own realm secure from their Enemy? And though he be now their foe, are not they and he of one kin? Vengeance calls me hence, but even were it otherwise I would not dwell longer in the same land with the kin of my father's slayer and of the thief of my treasure. Yet I am not the only valiant in this valiant people. And have ye not all lost your King? And what else have ye not lost, cooped here in a narrow land between the mountains and the sea?
'Here once was light, that the Valar begrudged to Middle-earth, but now dark levels all. Shall we mourn here deedless for ever, a shadow-folk, mist-haunting, dropping vain tears in the thankless sea? Or shall we return to our home? In Cuiviénen sweet ran the waters under unclouded stars, and wide lands lay about, where a free people might walk. There they lie still and await us who in our folly forsook them. Come away! Let the cowards keep this city!'
Long he spoke, and ever he urged the Noldor to follow him and by their own prowess to win freedom and great realms in the lands of the East, before it was too late; for he echoed the lies of Melkor, that the Valar had cozened them and would hold them captive so that Men might rule in Middle-earth. Many of the Eldar heard then for the first time of the Aftercomers. 'Fair shall the end be,' he cried, though long and hard shall be the road! Say farewell to bondage! But say farewell also to ease! Say farewell to the weak! Say farewell to your treasures! More still shall we make. Journey light: but bring with you your swords! For we will go further than Oromë, endure longer than Tulkas: we will never turn back from pursuit. After Morgoth to the ends of the Earth! War shall he have and hatred undying. But when we have conquered and have regained the Silmarils, then we and we alone shall be lords of the unsullied Light, and masters of the bliss and beauty of Arda. No other race shall oust us!'
The Silmarillion - Chapter 9 "Of the Flight of the Noldor"
For reference, these two passages were based on a section from the Narn (War of the Jewels p166) and a section from the Annals of Aman (Morgoth's Ring p111-112), respectively. The published text is essentially just a more polished version of the originals, but it's worth noting that the Fëanor's speech had one extra line: "But by the blood of Finwe! unless I dote, if the cowards only remain, then grass will grow in the streets. Nay, rot, mildew, and toadstool."
A battle speech is a specific literary genre, and follows specific patterns. The codifier for this is Thucydides’ Histories; most Greco-Roman and modern battlefield speeches, both literary and historical, follow this same pattern:
See, for example, Patton's Speech to the Third Army.
Tolkien doesn't have any battle speeches of this sort in his work. Théoden's poem, and much of Rohirrim culture, comes from the Anglo-Saxon tradition. You can find poems in this pattern in works like Beowulf, and being specific to the Anglo-Saxon/Rohirrim culture, it would be surprising to find Elves speaking this way.
