Since all of the "number of things" words all follow the same pattern (number plus つ), you really just have to remember the part before the つ (and then remember that the つ is in all of these). All of the readings are the kun'yomi reading, which means we'll have to use a mnemonic to remember them (you know the on'yomi reading of the kanji portion).
What thing do you have seven of? The seven things that you have are seven Nanas (なな). These are your grandmas, cloned. Just think, "It's lucky to have seven nanas. They can all cook my favorite foods for me!"
There are seven apples in a box.
Just the two of us ate seven melons.
After I count to seven, I will be a woman.