My cakes lean. I level them with the small wilton leveler. It's all I have right now. I move it side to side to just inside the edge of the cake and then turn the cake to do that all round. Once that is done I move it farther in still moving side to side until it's finished. I do this for every layer. Once I remove the top I go over it again just to make sure. Sometimes I torte, most of the time I don't. Sometimes I use a filling between layers but most of the time I just use icing between layers. They look level when in the individual tiers but when they're all stacked on top of each other, as in a three tier cake, they lean. Do I need to get a level out? I use the straws for supports. I insert one, lift it out and cut it just below the top. I use that one straw to cut all the others. I do this for every tier that needs supports for the next tier. I use the cardboard circles/squares under each layer and MDF as my cake board on bottom. I let my cakes rest after baking, usually over night or freeze overnight then rest several hours to defrost. Once filled and/or crumb coated I let them rest again or freeze then rest for hours. When I freeze depends on my time line. The cakes always get to rest on the counter though before the final icing. Sometimes I put something on top to compress them a bit, too. I'm having huge issues with leaning and it's making me want to give up.
Definitely get a level to use for cakes only...takes all of the guesswork out of it. I've heard some people having issues with the Wilton levelers not cutting level. Personally, I had the worst time with leaning cakes, until I figured out that my table was not level! (cakes were level when on the table but as soon as I moved them to another table, they were leaning.) HTH
Yes. Use a level. You can't just "eyeball" a cake to tell whether it's level or not. I bought mine (laser) for under $20.00 at Lowe's . Great investment.
Also, be sure you are cutting all your dowels (or whatever you are using for support) all the same exact length. Be sure to put a board between each tier too.