I'm looking to employ some students for part-time and/or short term work, like a couple of weeks. Likely they'll work from home (desk-based internet research).

How much paperwork is involved in doing this? Is there any scheme for employing them without going through the same hoops as for a full-time permanent position (i.e. full payroll, taxes, insurances, pension etc). Having to do that would no longer make it worthwhile as the setup effort is bigger than what the work done would be worth.

Hire them via an agency like Adecco
That is what i do.....

How about hiring them through a freelancers website. I use http://Odesk.com which is for more technical freelancers but you could also try http://elance.com

When you hire someone via these sites you are still engaging in a direct relationship with the freelancer. If the freelancer is not really a freelancer (i.e. doesn't have multiple employers, isn't correctly registered etc) then the tax office still sees you as the employer and liable to deal with all tax-related issues as such. In other words they will fine you big time if you don't sort that out properly - waving an invoice at them is no good. Its a big un-mentioned part of the business model of odesk, elance, pph etc.

You can get away with that to some extent if its abroad (nobody will know) but for hiring locals its dicey.

Can you not just pay them cash for the work they produce?

i.e. they sell you the research for what you would have paid them as a wage...

saves messing about with employment contracts and tax and stuff.

I have people working for me few hours just once in a while. I pay them cash and ask for a receipt where it is mentioned: date, hours worked, name, address and amount. No need to do a contract. In my case I also do an insurance against accident, which is a general insurance for temporary workers and it is pretty cheap. You pay a fixed amount at the beginning of the year and at the end the insurance company based on the hours declared do the balance. All insurance companies can do it.