Whoever traded you that Quagsire had no idea what he was doing. Quagsire's movepool isn't that bad really. It just needs to be treated properly. Swampert indeed has better stats for a Water/Ground type, but Quagsire having either Water Absorb (good for double battles with something that knows Surf) or Unaware (if you're really technical) is better than Swampert's Torrent (unless you have Damp, which is close to useless). Here's my suggestion:
As for stats, you should be more foccused on ATTACK. Giving it special moves won't make it very powerful. An Adamant nature is my suggestion. Don't try raising its speed either - it's not going to outrun anything, even if it is scarfed.
Earthquake - which is oddly a physical move. It is basically 150 power because of Quaggy's ground type (STAB). This is the most important move for it.
Waterfall - also oddly a physical move. Adds STAB. Do not use Surf over this, as it is a special move.
Ice Punch - good against types that cause trouble (Grass and Dragon). Putting Quaggy up against a Grass type is one of the worst ideas, but as a last resort, use this. Don't waste an Ice Beam TM on Quagsire - it's a special move.
As for the last move, I'd suggest a Rock-type move like Stone Edge or Rock Slide (both physical), or anything that has a decent amount of power, belongs to a different type than any of the above, and is physical. If you want to be more technical, Curse would be a good thing to have, as Quaggy's speed is pretty much useless, but its Attack and Defense are rather high.
As for items, I'd suggest a Rindo Berry (Quagsire's only chance against Grass Types, and as Grass is its only weakness). I've seen suggestions where people give it leftovers, but I honestly don't see how that affects it much. Don't try choice-scarfing Quagsire, as it'll still be outrun by most opponents, and its movepool can have supereffective against a diverse range of Pokémon. The only thing I can suggest to fix its speed is a Quick Claw, but that's a bit too risky.
Quagsire is probably best used in doubles, if it has Water Absorb (assuming that you're playing a Gen IV or V game). If you use it with a Flying-type that knows Surf, it'll gain HP in battle. Using Earthquake along with the Flying-type's Surf can be a pretty damaging combination. If you would rather be technical with it (and have access to the Dream World), I'd use one with Unaware, but there are better Pokémon out there for countering stuff like that, like Clefable and Swoobat (that thing's really creepy though), who both have Unaware. Don't use Damp. Explosion and Selfdestruct aren't used commonly enough.
-The Magikarp Avenger