ساڑھے is a local suffix, added to numbers three and above, to denote "-and a half", as well as "half past-".
Thus:
ساڑھے چار سال => four and a half years,
ساڑھے دس بجے => at 10:30, at half past ten

To denote "one and a half" or "half past one", please use ڈیڑھ , which itself is complete and no extra "one" is necessary.
Similarly, use ڈھائی for "two and a half" or "half past two".

آدھا is of Sanskrit origin, and is commonly used to mean just half or incompleteness of something:
آدھا حصہ مجھے دے دو => give me half the share

نیم is of Persian origin and mostly used to denote "half-", "semi-", "mid-", "incomplete" or similar ideas:
نیم سرکاری => semi-official
نیم حکیم => inexperienced physician
نیم شب => midnight ; also : آدھی رات

نصف is of Arabic origin, and is more formal or technical in nature, used in specific cases to mean "half-" in compounds:
نصف روزہ سفر => half-day tour
نصف سالانہ => half-yearly
نصف ملین ڈالر => half a million dollar

I hope the explanation would be helpful to all, and I welcome any comments on it.


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Note added at 1 day7 hrs (2009-11-21 01:25:59 GMT) Post-grading
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Special thanks to KMP88 for choosing this answer, and thanks also to all who have spent time to read my long answer. Best regards to all !!