So the question is: How much can a Battle Barge and Three Strike Cruisers hold? In terms of Space Marines, vehicles, etc?
Well, a Battle Barge is roughly equivalent to a Battleship of the Imperial Navy, with a number of changes. I would say it could probably hold around three full companies of Space Marines, their vehicles, gear, drop pods, ships, etc. Maybe four in a pinch if they really needed to pack it in. The problem is not how many space marines they can have in them, they could probably have way more than three hundred, the problem is the required cargo bays for all of their equipment, war-gear, vehicles, and not to mention places where Dreadnoughts and Terminator Armor can be stored and cared for.
As for Strike Cruisers? I would guess about only one Space Marine company per Cruiser. Again it isn't the problem of holding the Space Marines themselves, but rather all of the war-gear etc that they need.
So, you could probably get away with about 5 companies of Space Marines, or about half the Chapter, with a Battle Barge and three Strike Cruisers, but only just. 4 companies would be optimal. You could add more than 500 Space Marines, but any extra would probably be lacking in proper gear and equipment. Just my thoughts and estimates. Also, Commander Hair-Gel, hahaha. That gave me a good laugh.