A while back I wrote a blog post about the different ways you can control the Datasource of your multilist and treelist fields (with and without search). The third technique listed for fields with search is what I think you are looking for:
Search in two or more places of the content tree (Fields with Search):
StartSearchLocation={110D559F-DEA5-42EA-9C1C-8A5DF7E70EF9}&Filter=_path:110d559fdea542ea9c1c8a5df7e70ef9|_path:3d6658d8a0bf4e75b3e2d050fabcf4e1
For your implementation:
StartSearchLocation={Website.ID}&Filter=_path:[News.ID (guid form; no brackets)]|_path:[Events.ID (guid form; no brackets)]|_path:[Articles.ID (guid form; no brackets)]
Search in two or more places of the content tree (Fields without Search):
If you are using a Multilist field (without search) then I would do the following:
DataSource=/path/to/source/1|/path/to/source/2
For your implementation:
DataSource=/sitecore/website/news|/sitecore/website/events|/sitecore/website/articles
I would also add that the Treelist with Search field has been deprecated in later versions of Sitecore 7, so if that is the field that you are using then I advise changing to the Multilist with Search field. If you are using a standard Treelist field, then Ahmed's answer may be viable as well, depending on your use case.
Let me know if you have any questions. Good luck, and happy coding! :)