A few things:
These are not sung in Orthros, certainly in parish use, because full Sunday Orthros in the Byzantine tradition takes like three hours, and this is not part of the usual cutdown of Orthros used in Greek or Antiochian parishes. Some monasteries will sing them sometimes during Orthros, based on the igumen (abbot).
The 7th and 8th Odes are from the book of Daniel - Song of Azariah (Benedictus es Domine Deus patrum nostrorum in Latin liturgical use, which you're apparently familiar with) and the Song of the Three Children (Benedicte); I believe both of them are only found in the Septuagint. (thus you'll see them in the Orthodox Study Bible which uses the Greek edition of the Law and the Prophets (Old Testament) but not in most other Bibles which use the Hebrew Masoretic text)
Anyway, the structure of use would go something like this (I'm using the Heirmos and first two stanzas of the Akathist Canon, using the GOArch DCS translation). [EDITED TO ADD: this is the raw, basic setup. In reality there are rubrics for how and where to place the verses, in full monastic use - where the recite the Odes and several canons a day - but that does not matter here and if you are interested in praying this I'd just straightway pray the Odes]
Ode 1
[Song of the Sea, NIV translation because it's what I could easily find]
will sing to the Lord,
for he is highly exalted.
Both horse and driver
he has hurled into the sea.
2 "The Lord is my strength and my defense;
he has become my salvation.
He is my God, and I will praise him,
my father's God, and I will exalt him.
3 The Lord is a warrior;
the Lord is his name.
4 Pharaoh's chariots and his army
he has hurled into the sea.
The best of Pharaoh's officers
are drowned in the Red Sea.
5 The deep waters have covered them;
they sank to the depths like a stone.
6 Your right hand, Lord,
was majestic in power.
Your right hand, Lord,
shattered the enemy.
7 "In the greatness of your majesty
you threw down those who opposed you.
You unleashed your burning anger;
it consumed them like stubble.
8 By the blast of your nostrils
the waters piled up.
The surging waters stood up like a wall;
the deep waters congealed in the heart of the sea.
9 The enemy boasted,
'I will pursue, I will overtake them.
I will divide the spoils;
I will gorge myself on them.
I will draw my sword
and my hand will destroy them.'
10 But you blew with your breath,
and the sea covered them.
They sank like lead
in the mighty waters.
11 Who among the gods
is like you, Lord?
Who is like you-
majestic in holiness,
awesome in glory,
working wonders?
12 "You stretch out your right hand,
and the earth swallows your enemies.
13 In your unfailing love you will lead
the people you have redeemed.
In your strength you will guide them
to your holy dwelling.
14 The nations will hear and tremble;
anguish will grip the people of Philistia.
15 The chiefs of Edom will be terrified,
the leaders of Moab will be seized with trembling,
the people of Canaan will melt away;
16 terror and dread will fall on them.
By the power of your arm
they will be as still as a stone-
until your people pass by, Lord,
until the people you bought pass by.
17 You will bring them in and plant them
on the mountain of your inheritance-
the place, Lord, you made for your dwelling,
the sanctuary, Lord, your hands established.
18 "The Lord reigns
for ever and ever."
[followed by the Akathist Canon]
I open my mouth and pray the Spirit fill it, like David said, * to pour out a good word to the Queen and Mother of God. * I will celebrate * her feast with joy and gladness * and sing to her merrily, lauding her miracles.
Most-holy Theotokos, save us.
O Maiden and Virgin pure, the great Archangel saluted you, * "Rejoice, living book of Christ, of which Isaiah foretold * that it would be sealed * to all men by the Spirit. * O vessel of joy, through you the curse on Eve shall be loosed."
Most-holy Theotokos, save us.
Rejoice, Virgin Bride of God! Through you was Adam restored to life * and Hades was put to death. O blameless one, rejoice! * Since you bore the King, * we say you are His palace, * the fiery throne of the Ruler of all. Rejoice!
[etc. Note there is no Ode 2 in most canons]
Ode 3
[Song of Hannah]
My heart exults in the Lord;
my strength is exalted in my God.
My mouth derides my enemies,
because I rejoice in my[
b] victory.
2
“There is no Holy One like the Lord,
no one besides you;
there is no Rock like our God.
3 Talk no more so very proudly,
let not arrogance come from your mouth;
for the Lord is a God of knowledge,
and by him actions are weighed.
4
The bows of the mighty are broken,
but the feeble gird on strength.
5
Those who were full have hired themselves out for bread,
but those who were hungry are fat with spoil.
The barren has borne seven,
but she who has many children is forlorn.
6 The Lord kills and brings to life;
he brings down to Sheol and raises up.
7
The Lord makes poor and makes rich;
he brings low, he also exalts.
8 He raises up the poor from the dust;
he lifts the needy from the ash heap,
to make them sit with princes
and inherit a seat of honor.
For the pillars of the earth are the Lord’s,
and on them he has set the world.
9 “He will guard the feet of his faithful ones,
but the wicked shall be cut off in darkness;
for not by might does one prevail.
10 The Lord! His adversaries shall be shattered;
the Most High will thunder in heaven.
The Lord will judge the ends of the earth;
he will give strength to his king,
and exalt the power of his anointed.”
[Akathist Canon]
Establish your servants who extol you, * O Mother of God, for they have formed * a spiritual choir for you * the living and abundant fount; * and graciously in your divine glory give glorious crowns to them. (2)
Most-holy Theotokos, save us.
Rejoice, blessed Virgin! You have borne Christ, * the Wheat that came forth from land unploughed. * The Table symbolizes you, * who held the Lord, the Bread of life. * Rejoice, O never empty well * of living water, O Bride of God![SD]
Most-holy Theotokos, save us.
For us the believers you have mothered * the unblemished Bull, the Lamb of God, * who takes away the sins of the world; * we therefore call you Heifer and Ewe. * Rejoice! You are the Mercy Seat, * from which forgiveness has come to us.
[etc, etc.]
If you want to read the Odes in full, highly recommend you pick up a psalter with the Odes (and organized into Kathisma!). The Greek psalters (iirc Apostoliki Diakonia and Phos) have them. Here are a few English ones: (my subjective personal opinion in parentheses)
Holy Myrrhbearers Monastery
https://svspress.com/the-kathisma-psalter-with-the-nine-canticles/ (RSV modern English Bible translation with some verses changed to reflect the Greek vs. Hebrew Bible passages. My personal choice)
Holy Transfiguration Monastery [full large blue book is out of print; the green pocket psalter that's still in stock does not have the Odes] (IMO this is the worst of HTM's translations, which I'm usually fond of. It's one of their earliest translations still in print - and is rough, and it seems they try to translate the Greek literally into overly traditional English)
A Psalter for Prayer
https://www.holytrinitypublications.com/a-psalter-for-prayer-2 (another traditional translation. It claims to be Miles Coverdale's psalter - the one used by the Anglicans and therefore a key part of English liturgical worship - with some verses corrected to conform to the Septuagint. IME, it's partly Coverdale, partly HTM, partly a new translation. It has a lot of extra material outside the psalter and the odes, ostensibly of Slavic use for personal prayer with the psalter. It seems nice but it makes it a bit cumbersome to use liturgically IMO).
[IMO it's regrettable the Orthodox Study Bible project has not published a Psalter organized into kathisma with the Odes]
ETA: here's a free PDF psalter. It's a modification of the King James psalms to ostensibly conform to the Septuagint. I probably would start here and go to the Hoyl Myrrbearers if you like more contemporary language.
http://www.synaxis.info/psalter/5_english/c_psalms/kjvsept.pdf
