I always read about the merits of various rifle actions, including strength, safety in terms of gas escape if a case rupture occurs, etc. However, I don't think I have ever read anything about shotgun actions.

I have a Browning Citori over-under, a Benelli Field 90 auto, a Remington 870 pump, and an Ithaca 37 pump. All these are newer guns (no more than 7 years old). What is the safest action in terms of strength, etc?

The lock-up strength of virtually any shotgun far exceeds that needed to simply contain the chamber pressure and resulting bolt thrust.

What is much more important is how the action handles escaping gas and particles when a base wad fails or rim blows out (a phenomenon pretty well confined to the good old paper tube days).

I grew up with an old Mossberg bolt action. The action was plenty strong, but when an old paper shell decided to blow a piece of the base wad out the side of a split rim, the gun's stamped metal extractor would get in the way and sometimes get bent nearly double, while spraying me, a left-handed shooter, in the face with debris. Just hammered the extractor out straight again and went back to missing doves.

As to the models you mentioned, I have no idea which would handle a blown base wad best, but a blown base wad is almost unheard of these days.

With really dangerous overloads, a chunk of steel will be blown out of the barrel of the shotgun over the chamber before the action will let go.

P.S. In regard to absolute strength, I would have to assume that the Browning Citori, which is used as a basis for some double rifles, would be the strongest. Its barrels would be thinner than the repeaters, however, and therefore more prone to rupture.

With its solid top receiver and bottom ejection, I would think that the Ithaca would protect the shooter very well from escaping gas.