Just listened to it [several times] and the words listed above are indeed what they're singing. I've fixed the layout to match how they break it up with the melody. Those that don't seem to fix are sung pretty fast to match the melody.

DRINK THE NIGHT AWAY
We set sail at half-past morn,
Looking for a new tomorrow,
Don't know when we're coming home,
So we'll drink, and we'll dance, and we'll drown our sorrow!

chorus:
Weigh-hey! Hey Laddie, hey!
Weigh, hey, hey! We'll drink the night away!

Now I don't know what there lies in store,
But it's better than this, that's why I'm willing,
To stake my claim on a foreign shore,
With me spoons and me fiddle, and half a shilling!

cho

I dreamt a place, I know it's true,
Where the dolphins play and it's always sunny.
The girls are brown and the ocean blue,
Less work to do, but you make more money!

cho

I must be off by morning's light,
I can hear our bo'sun's whistle blowing,
So it's one more kiss and one more fight,
And one more song while the beer is flowing!

cho

When the sky is grey, look out to sea.
When the waves are high and the light is dying,
Now raise a glass and think of me...
When I'm home again, boys, I'll be buying!

Cho X4 [last 2 a capella]