For non-tech managers I have fallen back on an analogy of building a house. Would they build one without blueprints, just taking bricks from a pile and putting one atop the other with a vague house-shaped idea in mind? If not then why won't they accept proper documentation before coding, design reviews, etc?
For unit test, you could try comparing it to quality testing the various house components individually before putting them together (bricks, cement, doors, windows, plumbing)
For those with any tech grasp at all, I mention that 30% to 50% handles error conditions and recovery (in mission critical embedded systems) and that you just can't test that without unit testing. E.G, if you only blackbox integration test then how can you - in a controlled and repeatable manner -test what happens when module A can't allocate memory at a given point, or a timeout expires deep in module C when waiting for a reply message from somewhere, or a database read which will normally succeed. Explain that by dummying out interfacing modules you can simulate their erroneous behaviour at will.
And, of course, I draw my favouriite graph with a $ symbol on one axis and a clock on the other. I beat management over the head with this at every opportunity to show that the cost of getting bugs out increases the later they are discovered (change a line in a requirement spec – 5 minutes; a few paras in a design doc – hours; several 100 lines of code (at code review or unit test stage) – days; finding the needle in a haystack bug and correcting it at system test – weeks).
It's not just unit test – you have to convince management – and your fellow developers – that the “unnecessary overhead” of documentation, reviews, testing ... s/w Processes in general (and that includes learning new tools) ... actually saves time rather than adding time to a project. In other words, it takes longer and costs more to get it wrong. Measure twice, cut once, etc
For unit test, tell them about continuous integration (http://en.wikipedia.org/wiki/Continuous_integration). I strongly recommend Hudson, but use whatever works for you. Explain that a regular build, whether nightly or with every check-in, can automatically pull unit tests from your VCS and run them, sending email or otherwise alerting to new code that broke existing tests almost as soon as it happens.
If none of that works, look for a new job (if you are in Singapore, or want to be, talk to me ;-)