According to my sources, the statute of limitations for most debts in Nebraska is five years. if the statute of limitations has indeed expired on these debts, then you can simply send the collection agency a cease and desist letter explaining that the debt is too old, and asking them not contact you again. If they contact you again, it would be to take you to court and that would be unlikely if this were a debt that's too old.
Having said that, I would recommend you confirm the statute of limitations with an attorney or your state Atty. Gen.'s office. In addition, if these are debts for student loans or taxes, or if the creditor has a judgment against you, then different rules apply.
Please make sure you keep good records of all your correspondence with these companies (start a file) and send your letters by certified mail, or with delivery confirmation.
Finally, since it sounds like you are dealing with multiple debts, I would recommend you at least familiarize yourself with your basic rights when dealing with debt collectors by reading our e-book or it least reading the first chapter of Debt Collection Answers online for free.
As far as your credit reports are concerned, collection accounts may only be reported for 7 1/2 years from the date you first fell behind with the original creditor - regardless of whether you paid the bill or not.