My first character has been panning out quite nicely guys.

Nord Thief who specializes in sword combat, archery, and stealth. If I had to take a guess I would have to say I am level 7 or 8 and I just closed the first oblivion portal. I explored the landscape and hit random dungeons for 10 hours before starting the main quest.

My problem is in hand to hand combat my sword seems like it is just bouncing off enemies. It knicks away health at a rate that's almost not noticeable. My blade skills have been raised high enough where I have unlocked the sideways slash that has a chance to disarm. My strength is also around 70.

I have been spending most of my points in Strength, Agility, and split between luck/endurance

From there the majority of my weapons are 1h Swords, Daggers, Bows, and a bit of magic (healing)

Is this how damage is supposed to be? Sneak attacks with the bow deal a decent amount of damage, but after that it takes about 17-20 sword slashes or 10-12 more arrows to kill even a scamp.

First off, when you level up, the baddies get stronger as well. The higher your level, the more swings it'll take to kill something, generally speaking.

Also, your stamina plays a large role in melee combat. If you stamina is almost depleted it will take MANY MANY more swings to kill something than if your stamina was full.

Other than that, is your sword almost broken? Try to keep it repaired as that affects your damage as well.

What kind of sword are you using, and what condition is it in? Do you have the difficulty slider set higher than center?

Your description matches what one would experience with the difficulty turned up to an "unreasonable" level. Unlike in some games, the difficulty slider in Oblivion doesn't change anything but relative combat damage.