Marking the eggs as either "cage free", "free range", or organic doesn't have anything to do with what store is selling the eggs.
The producer must meet criteria strictly defined by the USDA in order to use those labels. And using them means that the USDA is inspecting their facility to ensure their criteria are being met. Cage free simply means that the birds are not stored in the 1X1X1 cages that most commercial egg layers are kept in. They're housed in large barns and never go out side. Free range is similar, but the birds are required to have access to the outdoors. Not necessarily grass, and they aren't required to actually BE outside for any length of time. The label you're looking for is "pastured". That means the bird is on grass and is able to eat the grass and bugs they find. Your best bet is to buy a pair or trio of hens and keep them yourself. It's cheap and easy to maintain a backyard flock, and kept a cage about the size of a rabbit hutch, they can often find enough forage to sustain themselves through the spring and summer without extra feed (providing you move the cage), and fertilize your yard in the process. Chickens are not zoned against in most towns, either. I raise chickens myself, and I can tell you one thing. A chicken egg that's been snatched from the laying box is a better egg than ANY egg from ANY grocery store, regardless of the the useless label on the carton.
What do you mean by "really free range?" if you mean, uncaged, in a gigantic stinky barn with hundreds of other uncaged chickens, yes they are free range. If you mean out on their own in a field with green grass etc... I doubt it. Free range pretty much means that if they get an open wound in the barn, the other chickens can get to them and peck them to death.
If they are the Aldi brand, the only way to find out would be to first find out who their supplier is. If you contact Aldi, they should be able to tell you this. Then you can search for information on that particular supplier and find out their track record. It is unfortunate, but as rainnsurf stated, companies take advantage of these labels in order to find the loopholes. A group like Aldi that is not promoting organic, non-GMOs, etc. is not likely to put the consumer first. You're better off buying free range from Trader Joe's, Whole Foods (more expensive), or a local health food store in order to get peace of mind. Although much more expensive, if the eggs are USDA organic, you shouldn't have any worries about buying them, no matter what store they are from.