The real strengths that Malzahar has lies in his ability to gain MASS AP. At the lower levels it's all about watching you mana and not dieing. if you can go the first 10 levels without dieing you should be 2 to 3 levels above everyone else. The real advantage is that with the spell pen you should be rocking people when they group up. Two AOE's plus one that will jump from kill to kill. Also once you hit 20 stacks on Mejai's you can drain a none tank for 2/3 of thier life with your ultimate. Tanks I usually hit for about 2/5 of thier life on a pull. If you can drop all three and hit with an ultimate it's game over for who ever your hitting.

Pluses:

High AP
Mass AOE
Silencing
traping ability
Finisher

Con's:

Mana issues at low levels
1vs2 he gets wrecked
defensless when his Ulti is on cooldown

When playing malz it's almost a must to be in the middle. If your not in mid then focus on 'w' to clear out the bushes. Other wise this is how I roll.

first six levels:

Focus on not chasing because without boots your relying on the long game
Keep Null Zone up on the field, this is your distance keeper
timing with the Malefic Visions is a must to get it to bounce to the other guy
make sure that you throw your fire dot once it comes up for your +10ap

level six to 12

You now have your stunner but unless you can catch him on the null zone with the Malefic Visions on him it's usless until you get to lvl two
By now your ap should be up and your spell pen should be at +20% from the boots so spam your Malefic visions.
You should also have your Mejai's soulstealer so it's time to start jumping lanes for the gank

level 12 to 18

At this point you should have 6 to 10 stacks on Mejai's and quickly climbing
with your items you should have 600 AP by lvl 15 and be 3 levels above everyone else
You should be grouping and snagging those kills as they try to run away
once you hit 20 stacks you should be GOD like with over 800 ap