How do I change the color of Strikethrough without changing the color of the text?

You can change the color of underlines separately from the text through the UI (in the Font dialog), but the OP wanted to change the color of strikethrough.

You could use a macro such as the following to apply red underlining to a Selection:

Sub ColoredUnderline()

Application.ScreenUpdating = False

Dim StrTxt As String, Fld As Field, Rng As Range

ActiveWindow.View.ShowFieldCodes = True

With Selection

  StrTxt = .Text

  Set Fld = .Fields.Add(Range:=Selection.Range, Type:=wdFieldEmpty, _

    PreserveFormatting:=False, Text:="EQ \s\do8(\f(" & StrTxt & ",))")

  .MoveLeft wdCharacter, 2

  .Delete

  Set Rng = Fld.Code

  With Rng

    .Font.ColorIndex = wdRed

    .Start = .Start + InStr(.Text, StrTxt) - 1

    .End = .Start + Len(StrTxt)

    .Font.ColorIndex = wdAuto

  End With

  .Fields.Update

End With

ActiveWindow.View.ShowFieldCodes = False

Application.ScreenUpdating = True

End Sub

You could of course, change both the underline colour, currently set via .Font.ColorIndex = wdRed, and the text colour, currently set via .Font.ColorIndex = wdAuto. Because the field displays the underlining below the text instead of running through character descenders, line heights will increase slightly. Changing the 8 in the code affects how high above/below the line the underlining will be.

Notes: If the range spanned by an EQ field exceeds the amount that be displayed on a single line or spans a paragraph break, the result will be an 'Error!' display in the document. Similarly, if the range spanned by ab EQ field includes any line-wrapping or a manual line break, the entire field will be pushed to the next line - a manual linebreak will be displayed as a narrow vertical rectangle in the output.

I don't see a simple way to create a macro that creates the EQ field (which doesn't mean that creating a macro would be impossible).

In the long run, posting a suggestion for http://word.uservoice.com is probably a better idea (or you can vote for any existing suggestions).

The solution is remarkable. It would be perfect though if Stefan could precede the overstrikes with a macro, or just embed a macro, to overstrike the complete text. As is, one needs to count the number of characters that need to be struck through.