I don't play harp, but I have some thoughts. (I have a friend who has five harps.)

First, you should talk to the previous owner and find out if the harp has been played much. No point in "breaking it in" if it doesn't need it.

Also, where has it been stored? If it was kept (worst case) in a garage in Death Valley, then you need to think about gently re-hydrating it. I leave the other permutations on this theme up to you.

Have you turned it upside-down and looked for a maker's name on the bottom or inside the sound box?

Tuners are sure nice, but I have found that when an instrument is way out of tune, a simple electronic tuner can't deal with it. If a D string, let us say, is playing something near B-flat, the needle just swings wildly back and forth. (This happens to me when I put new strings on my guitar.) In this case, I go to the piano, find about where the string is, and gradually move it up to pitch, matching the notes of the string to the notes of the piano as I go. If you don't have a piano, I hope you can find a friend who has one. If you are worried that the tension will be too much, you can stop short, of course.

The seller may have loosened the strings for shipping, and they may all be quite flat.

Actually, when I come to think of it, it's not just the tuner that can't deal with notes that are way, way off. My ears don't handle it well, either.

Hope this helps. I would like to hear about what you are doing with your new harp.