Is the ILS VOR located to the right of the Runway?
Did you tune the ILS or the VOR there?
Don't mix them up as this is a common error because the readings show up on the same instruments, but, from the technical side, both things only have very few things in common.

The VOR would be placed anywhere, sometimes on the airport aerial of course, but never really aligned that precisely to allow an ILS-like accuracy. The VOR measurement also is different, allowing huge ranges but not so precise readings to actually autoland with it.
See it as a rough guidance, surely able to assist during the approach, but the minimums are way higher than on ILS landings there, for good reason. As said, autoland on VORs is not allowed (and shouldn't be possible too).
E. g., if you set that Course needle to the wrong setting while flying with a VOR, you will actually fly the wrong Course. Doing the same when having tuned the Localizer won't harm you though, the plane would follow the fixed Localizer heading as long as it can receive it and is able to follow, precisely.

The ILS is precisely aligned with the runway centerline (=Localizer component of the ILS), at least in most cases. All special cases are marked as such and carry notes like "offset Localizer!" or something not named "ILS".
You'll see some of those at high surrounding terrain airports where you are guided on the Localizer until a certain height and "break off" from it when reaching the lower limits, to fly the rest of the approach visually. Take Innsbruck for example. A famous approach, not named "ILS" but using some of the components there.

So while all normal ILS related things are always bound to that special runway (sometimes in both directions), the VOR stuff is a more general aid on the approach and might give you that offset you spoke of.

If you get an offset while using the ILS, check your scenery file for the right numbers there. Maybe it's misaligned.
The 727 itself is able to follow the ILS precisely, by design. No autoland though.

Thanks folks, I will check my settings tonight. I think I may have dailed in the VOR not the ILS.