CFrame.new from Vector3.Value Fix?

To change the position you need to use a Vector3 value, to change it with CFrame you need to change the part's CFrame. e.g.

workspace.Part.Position = Vector3.new(0,0,0)
--Both work, but CFrame can clip through other objects.
workspace.Part.CFrame = CFrame.new()

Now with that knowledge lets fix your script.

function onClicked()
    if script.Parent.CFrame == CFrame.new(0,0,0)--[[Off Value]] then
        script.Parent.CFrame = CFrame.new(on.Value)
        end
    if script.Parent.CFrame == CFrame.new(0,1,0) --[[On Value.]] then
        script.Parent.CFrame = CFrame.new(off.Value)
    end
    end
script.Parent.ClickDetector.MouseClick:connect(onClicked)

Please edit the parts next to the green comments.

Hope it helps.

You're setting a Position (a Vector3) to a CFrame. CFrames aren't Vector3s, so you can't do that.

To get the position of a CFrame, use its .p property -- read the wiki.

However, it would be better to set the CFrame, rather than set the Position, because Position behaves rather poorly.

Thus the best solution would simply be

function onClicked()
    local on = script.Parent.Vector3.On
    local off = script.Parent.Vector3.Off
    if script.Parent.Position == off.Value then
        script.Parent.CFrame = CFrame.new(on.Value)
    end
    if script.Parent.Position == on.Value then
        script.Parent.CFrame = CFrame.new(off.Value)
    end
end
script.Parent.ClickDetector.MouseClick:connect(onClicked)

Remember to tab your code correctly

Of course, it's not a good idea to compare the Positions, or to compare to on and off when they're opposites. Use a boolean variable:

-- Something like this:

local on = false -- Or true, whichever it STARTS as

function onClicked()
    local go
    if on then
        go = script.Parent.Vector3.On
    else
        go = script.Parent.Vector3.Off
    end
    script.Parent.CFrame = CFrame.new(go.Value)
    on = not on -- true --> false --> true
end
script.Parent.ClickDetector.MouseClick:connect(onClicked)