A couple of things that may be prudent to remember are that size categories include a range of different sized creatures and items. Remember that a 5ft elf is considered to be medium sized in the same way that a 7ft half orc would be. Surely we can all agree that to the elf a 'medium' sized great sword might be shorter than a 'medium' sized great sword for the half orc.
Fans of history and avid patrons of musea and reenactments will know that the blade of a great sword is often less long than that of a bastard sword, the additional hand grip above the hilt accounting for the extra length of the weapon. D&D does not actively provide for the reason behind this feature on the weapon, but this is where the flair of role play comes into its own. (Rather than an overhand swing, your character might flip the sword horizontally, grab the upper grip, and stab the charging orc)
To that end, if your character is on the top end of the 'large' size category, and the huge great sword is at the lower end of the 'huge' size category, the weapon need not be inappropriately sized to take with you into a tavern with respect to your own considerable size. Of course, allowing an Ogre into a medium-sized tavern poses problems of its own, as some of my peers have mentioned. Moreover, it would not be unusual for a proprietor to insist on weapons being left at the door. (There is good fun to be had roleplaying with the coat check girl when she asks you to part with your +2 flaming dwarven ugrosh!)
Also note that great sword designs, including their length, may vary based on who created the weapon. A dwarven great sword might be more stout and wide than its elven counterpart.
I would suggest you make a decision in-tune with the campaign of which you are a part. If the weapon is going to be a recurring problem, sell it, tell stories of it, perhaps even emulate it by having a slightly smaller (one size category) copy made, and use that instead. The people around the table will respect you a lot more if you don't insist on carrying around an item blatantly obvious meant to overcompensate for other shortcomings. (your ogre's poor charisma score perhaps, or poor dental hygiene)
One of my characters faced this same problem once. It was overcome by role play and compromise, not a desperate grab at rules which do not readily exist (though illustrations exist, no specific rules are in place governing the length of a great sword).
D&D is about having fun, I suggest you do just that.
