I keep getting my ass handed to me by weak beasts (i've just started the game) because my weapons wont hit the opponent for more than the first hit. I uninstalled all my mods and I still haven't fixed this issue, can anyone provide any assistance?

It's not a bug. Weapon hits rely completely on your character skill. Make sure you're using a weapon type you're skilled in. You should start out with at least a skill of forty in your main weapon. Also, fatigue is extremely important. Make sure it's full or near full when in combat (and when you're doing pretty much anything else), otherwise you won't hit anything.

If you follow these, you should be fine. You'll still miss a lot, but you should hit a decent amount. As you level up, it'll get easier and easier. The turning point will be around level 5-7, when you get a bit of power.

Thank you very much, my friend. I did fear I was just victim to Skyrim and Oblivion's 'run and kill things!' approach, thankfully I have a nice armour to protect me. Is there an easy way to train up the weapons without getting killed every 10 seconds?

There are weapon trainers for most types in Balmora. If you have spear or shortblade, you can buy a weapon enchanted with the bound version for under 200g (gives a 10 point skill boost) also in Balmora.

Welcome to the world of Morrowind. You should definitely rely on what skills you have set as your major and minor skills, as you will be able to use those more efficiently than your miscellaneous skills. Once you level up a few times, then slowly chip away at your minor skills if you wish to do so. As a beginner, stick to what skills are the highest.

As a beginner, I advise you to have atleast 1 primary melee skill. Find a decent weapon appropriate to that skill and swing it!