There are several reasons why barrels are off-center, and sometimes oval.
1. The tubed blanks are not square to the tube. When the nut in the mandrel is tightened, the angled ends of the barrels bows the mandrel. This is why they sell pen mills, although there are other ways to square a barrel to the tube.
Sanding against a 90 deg miter will not work, UNLESS you have managed to dril the hole absolutely straight thru the wood. That seldom happens!
2. The tailstock is overtightened, forcing a bow on the mandrel.
3. To some extent, this also can happen when the nut is tightened too much.
4. The mandrel is bent. Probably a result of any or all of the above.
5. The tailstock is out of alignment with the spindle.
6. The bushings are too loose on the mandrel. This can happen when you use a bushing with a hole much larger than the mandrel. For example, PSI mandrels have a smaller diameter than those from other sources. Their bushings are made to fit their mandrels. Berea, Woodcraft, Craft Supplies, and others are of a better diameter. PSI bushings usually fit them, because they are a loose fit on the PSI mandrels. A good mandrel is about .246" diameter, same diameter as a "D" drill bit.
7. The live center does not fit the end of the mandrel. The hole in the end is usually designed for a 60 deg included angle taper. Most woodworking live centers don't fit very well, and will get worn out.
This is what I would do:
1. Put the EMPTY mandrel in the spindle. That is, if you have one with a Morse taper. Otherwise just mount it whatever way it is supposed to. Push it all the way in BY HAND.
2. Bring the tailstock with the live center in it to about 1/16" from the end of the mandrel. You want a little clearance. Tighten the tailstock.
3. Rotate the spindle BY HAND, while looking at the end of the mandrel. You will be able to see whether it is properly aligned. If it is bent, you will be able to see the end of the mandrel going around in a circle. Straighten it if necessary, or get a good mandrel.
Proper way to mount a mandrel:
1. After squaring the barrels, mount them in the mandrel with the proper bushings. Snug the nut, but DO NOT TIGHTEN IT.
2. Mount the mandrel in the lathe.
3. Bring the tailstock in position with a little clearance. Tighten it.
4. Advance the live center with the wheel until it contacts the mandrel. If you are using a Morse taper, this will finish seating it in the spindle. DO NOT overtighten. Back it up a little, and then just advance it until it is seated inside the hole at the end of the mandrel, and there is no play.
5. Now that the mandrel is straight and secured, tighten the nut at the end of the mandrel. Finger tight is usually enough !!!! That is why it is round and knurled !!!
Make sure the tools are sharp, and that the tool rest is positioned properly.
Don't ask me how I know... been there, my friend !!!
Hope this helps !!