Son of a Gun -
When a ship laid over in port, and the crew restricted to the ship for any extended length of time, wives and 'Professional' ladies were often allowed to live aboard along with the crew. Infrequently, but not uncommonly, children were born aboard, and a convenient place for this was between guns on the gun deck. If the child's father was unknown, they were entered in the ship's log as "son of a gun".
Betwixt the Devil and the Deep Blue Sea -
The devil seam was the curved seam in the deck planking closest to the side of the ship and next to the scupper gutters. If a sailor slipped on the deck, he could find himself betwixt the devil and the deep blue sea.
Let the Cat Out of the Bag -
Possible 1) In the Royal Navy the punishment prescribed for most serious crimes was flogging. This was administered by the Bosun's Mate using a whip called a cat o' nine tails. The "cat" was kept in a leather or baize bag. It was considered bad news indeed when the cat was let out of the bag.
Possible 2) Other sources attribute the expression to the old english market scam of selling someone a pig in a poke(bag) when the pig turned out to be a cat instead.
At Loggerheads -
An iron ball attached to a long handle was a loggerhead. When heated it was used to seal the pitch in deck seams. It was sometimes a handy weapon for quarrelling crewmen.
A Square Meal -
A ships crew were given meals (often 3 hence 3 square meals a day) served on square wooden platters.
Cut and Run -
Possible 1) If a captain of a ship encountered an enemy vessel, he might decide that discretion is the better part of valor, and so he would order the crew to cut the reefs on all the sails and run away before the wind.
Possible 2) Other sources indicate "Cut and Run" meant to cut the anchor cable and sail off in a hurry.