There are some brutal, ugly, and disgusting ways to do this … and probably some really good ways too, but the brutal, ugly, and disgusting ways are much quicker. ;-)
Here is one such way:
First of all, if these old documents are going to go to print (or PDF or whatever format you deliver in) again in the current form, make a good backup of all of them to removable media or however you/your organization handles backups. You should do this anyway, in case you ever need to pull the “clean” documents and use them anywhere, even if it's just to export some PDFs to throw into an annual report or something.
Then, take all the inDesign documents you need to “process” and put them in a folder that everyone knows is the only source for old text.
Open a document, select all the character styles, and delete them. Replace them with no style, but maintain the formatting. Repeat this with paragraph and object and table and cell styles as needed. Visually, the document should look the same, but when paste pieces into new documents, there will be no styles coming for the ride. Which means, of course, you'll need to apply correct styles in the new document.
Repeat this procedure for all the documents, and re-save them.
Of course, if you don't want to do this, you can always simply delete the imported paragraph styles when text is pasted into a new document, and replace with the correct styles. This is less work in the short term but probably more work in the long run.
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