Morphling's 3rd and 4th ability

If you want more health, pour your agility into strength, if you want more damage, pour your strength into agility. Keep in mind that, if you pour all your strength into agility, your health will be VERY low, whereas having extremely high damage. If you pour all your agility into health, you can survive quite a lot of Damage-over-time attacks, such as Viper's Ult.
One good way to utilise this is to pour your strength into agility and dealing huge DPS when you first see the enemy, then before the enemy can properly fight you back or other enemies can reach you, quickly pour agility back into strength to gain health boost to escape.
Morphling's 3rd and 4th skill can also be used in conjunction with his/her (not sure about Morphling's gender) 2nd skill - where Morphling will deal huge damage if his/her agility is 50% above his/her strength, or deal huge stun if his/her strength is 50% above agility.
(additional info from zozo) - Changing ALL agility into strength is actually making you less tanky than changing only a part of it (there is a critical point at about 14 agi). This is because 7 agi = 1 armor, and first few levels of armor give huge resistance vs. physical hits.

Seems like no1 wants to answer the ultimate skill part of the question, so I'm gonna give it a try:

You can use morph ult in multiple ways:

• To escape: Replicate something, do something to enemy heroes, then swap into the illusion (in my opinion this is kind of a waste but...)

• To confuse: Since morph ult takes normal damage, you can use it to confuse enemies (you can morph the initiator on your team and go between enemies (they will think you will initiate and waste some skills on it). Then of course you can swap into the image and go on from there. This is rather good vs. teams with expensive skills, or skills with high cooldown

• To deal damage: The illusion gives a decent amount of damage (50%), so replicating the most badass hero on the map will give u a pretty good damage (for example replicating a Nevermore [shadow fiend] that can get to hit for 500-1k damage, will allow your illusion to hit for 250-500 damage... that is... a lot). Also bear in mind that attack modifiers apply (like mana burn, desolator, etc.) - at least they used to, can any one confirm this is still valid (did not play for a while)?

• To explore... waste in my opinion, but are cases when it is useful

Fun fact: I don't know if this is still valid (used to be in dota 1): You cannot replicate yourself (this part is surely valid), but, if you have an illusion, you can replicate the illusion. So... with manta and illusion rune, you can have 6 morph at a time. BUYA PL. You don't outnumber morph!!.

4th ability is commonly used to escape or trick enemy heroes. for example, you could copy your teammate and then put the illusion in the base so when you are pushing/farming, you could easily escape when enemy's heroes come to gank you.

To trick enemy heroes using 4th ability, you could copy one of your teammate and then control them while enemy heroes are pushing. make it as realistic as possible and ask your teammate whose you are controlling to hide their real hero. chances are, the enemy team will probably engage the illusion thinking it is the real hero because of the tankiness of morphling 4th ability's illusion.

3rd ability is a little bit tricky. when you are farming/pushing/laning, you would want your agility more than your strength(around 70% to 30% is ideal). When you get banked by enemy heroes, you should start changing your agility to strength at the start of the gank to survive the gank.(keep in mind, you can still activate your 3rd skill even when you are stunned but not silenced. unless you activate your 3rd skill before silence.)