Foreword: I am focusing on DotA 2 since i stopped playing DotA 1 for quite a while now.
Stuns will hold Morphling in place but wont interfere with his morph ability in any way.
Chronosphere cannot stop his health gain.
Therefore you need a silence whether its an ability or an item to counter
Mantastyle does remove
Orchid can be good because even if
Morphling morphed into strength
Naixwill deal more damage.
Orchid works well too because of his burst damage.
Silencer is very good because his Ultimate is not a target spell and global giving your team the opportunity to counter
(thanks to Decency for mentioning those 2 in his answer):
Ancient Apparation is another great pick vs
Morphling because it prevents all kinds of healing including those from skills or items.
Mana Drain and
Hex can destroy an illusion immediately. Combined with his long disable overall and his nuke he can be a threat at all times especially with
To protect yourself against the enormous nuke of an
Morphling you should buy magic armor and a
Hand of God can be a substitute for
Mekansm. But since you need to heal yourself quickly i would not rely on another players reaction. Having both is even better)
BKB and spells like
Repel help a lot.
EB-Morphling needs as much agility as possible to nuke hard he wont have much HP while nuking. This opens a window for a
Blademail that can hit
Morphling hard and enables the possibility for a good trade (your support for their midgame-carry)
Linkens Sphere is annoying you should pick heroes who can afford wasting a spell to disable his
Linkens and have another good stun as a follow up.