As italy, you start with already a decent number of divisions. Problem is tech and IC.
So, in 1st 2 years (all 36 and 37) concentrate on reserach and conquer yugo and greece alone and develope IC ONLY in countries which are low in IC. Don't build any unit. Conquering yugo and greece will increase WE only of 5-6% (tested by myself). And try to reserach better ratio oil/coal otherwise you may find yourself low on resources once your industry is bigger.
Conquer Ethiopia but don't annex it so you keep having the low CG.
This would bring you in 'january '38 with a decent reseacrh for infantry and some IC.
From this on, slower research and increase build and add units.
1) Don't join Axis untill you are ready to join war (which is around '39 for Italy IMO). In most MP games i saw, Italy is screwed cause they join Axis too fast and when Germany enters war Italy isn't ready.
Italy's best advantage is that they can choose when entering the war (unless you decide to attack turkey). So at first go only on research since none can DOW you, no matter how weak you can be. Ad plan your enter in war when you're ready.
2) Your main front is, at start, Africa. Ask help to germany or Japan if needed, But conquer North Afrika. This is quite easy cause UK alone can't defend expecially if Germany borrows you some tanks. Conquer Africa (and suez) and mediteraean sea becomes your lake.
3) Do NOT try to conquer Malta: it's useless and you would lose too much manpower in the attempt
4) Do NOT attack Gibraltar unless UK players leave it undefended or with only one unit. Even with 1 unit it will be an hard match and do only if you have Spain under control and Germany providing you units.
The advantage to take Gbraltar is that basically, you can move all your units elsewhere since med is yours.
However, i think it's simply not worth. Even when Gibraltar is yours, nothing stops USA to land in ethiopia and take back suez which is hard to defend to US tanks.
5) Leave Ethiopia on his own. Leave there only militia. If you are fast enough to conquer north africa you may keep ethiopia. But Ethiopia is worthless.
6) Avoid direct battle against UK fleet, expecially if they have uberstack or many units in same sea spots. Your fleet must be used as deterrent and unload troops in mediterranean. Attack only when UK player moves small fleets. Move your fleet always all together.
7) Defend all beaches of italy with infantry, 2-4 each. And build few mech or light tanks to keep as reserve. Reember that UK player can land in Rome even if they have lost afrika.
If you do this, and german player helps you a bit, you should have north afrika secured and a decent army. From now on, my opinion is that Italy has just to help German player as he wants.
The best would be if Italy keeps defence of france and balkans letting all better german divisions to concentrate on SU.
Conquering Turkey is also good for IC, however do that only once afrika is secured and WE already at 100%. Otherwise to get 15 IC you give 80/100 IC to your enemies for lower CG.