Critical is like a point of no return. Or as you say having the potential to become disastrous.
So you need to do something RIGHT NOWWW!!!! Or else BOOOMM!!
Imperative is "just" of vital importance but not yet critical. It is however vital enough to start issuing imperatives or orders to get stuff done.
"It is imperative that we keep our troops moving, otherwise the enemy
will get there first. So we should give out orders now to keep on moving."
utmost is just very important without any need for any action yet. It's more long term. No orders need to be issued yet. It's not yet imperative. It is just extremely important. It's a comparison to something else. I.e. non or less utmost important things.
"It's just very very very important, it has outmost importance that we
keep this in mind for the future. So we should put this at the top of
our to do list."
Or per the definitions below. This item is furthest away from being non-important. Or it's of highest importance on our list. Yet that's all it is. Like the outmost pretty woman on the planet. No action is required but it might be desired none the less.
utmost |ˈətˌmōst| adjective [ attrib. ] most extreme; greatest: a
matter of the utmost importance. noun (the utmost) the greatest or
most extreme extent or amount: a plot that stretches credulity to the
utmost. PHRASES do one's utmost do the most that one is able: Dan was
doing his utmost to be helpful.
ORIGIN Old English ūt(e)mest ‘outermost’ (see out,-most).
imperative |imˈperətiv| adjective 1 of vital importance; crucial:
immediate action was imperative | [ with clause ] : it is imperative
that standards be maintained. 2 giving an authoritative command;
peremptory: the bell pealed again, a final imperative call. • Grammar
denoting the mood of a verb that expresses a command or exhortation,
as in come here!
critical |ˈkritikəl| adjective 1 expressing adverse or disapproving
comments or judgments: he was critical of many U.S. welfare programs.
2 expressing or involving an analysis of the merits and faults of a
work of literature, music, or art: she never won the critical acclaim
she sought. • (of a published literary or musical text) incorporating
a detailed and scholarly analysis and commentary: a critical edition
of a Bach sonata. • involving the objective analysis and evaluation of
an issue in order to form a judgement: professors often find it
difficult to encourage critical thinking in their students. 3 (of a
situation or problem) having the potential to become disastrous; at a
point of crisis: the flood waters had not receded, and the situation
was still critical. • (of a person) extremely ill and at risk of
death: he had been in critical condition since undergoing surgery. •
having a decisive or crucial importance in the success or failure of
something: temperature is a critical factor in successful fruit
storage. 4 Mathematics & Physics relating to or denoting a point of
transition from one state to another. • (of a nuclear reactor or fuel)
maintaining a self-sustaining chain reaction: the reactor is due to go
critical in October.
I got the definitions from the 10.9.2 OS X Mavericks built in dictionary.