I want to use swi14 to check statuses of workflows and let managers what needs to be completed and who has the workflow at the moment. 

Problem - there are old workflows that have the "in process" status, but are very old (early 2003) or broken workflows. 

My question is how do I get these workflows to a completed status and off this list? I have seen some of the responses to questions like this, but I don't want to delete anything out of the system. I want to keep the workflows as in, only change the status manually. 
 

You can use transaction SWIA to forward the workitem to the person who you want to execute. 

This transaction is for processing the workitem as Administrator. 
 

The old unwanted workflows can be Deleted Logically which puts them in Cancelled status. Display the top level work item, use menu path Goto-> Technical workitem display. On the next screen use menu path Edit-> Change. Then click on the 'Delete logically' button. 

You can also write an ABAP using the WAPI function modules to cancel Worklfows based on some selection like created date, Id, status etc. 
 

Thanks so much for the info, it worked like a charm! 

See Also
Workflow of Purchase Requisition Release Strategy

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