The trick with storing static electricity is that to do so it has to be transferred to a storage device all at once, rather than flowing in slowly like other storage systems - typically batteries. As static electricity represents the charge of an insulator, it is more easily lost to its environment before a transfer can be made and typical quantities of household accumulations of static electricity wouldn't amount to much at all. However, the solution to the storage of this energy lies with the help of another insulator, and that is the middle division of a capacitor.
Capacitors are essentially two conductors separated by a dielectric material (insulator). Although modern capacitors are two metal plates parallel to one another and separated with a thin insulator, the most simplistic early version consisting of a jar full of water and a metal lead. Charge held within a capacitor is actually held across the surface of the dielectric that is in contact with the conductor, and has a limit of how much charge it can hold before it allows the accumulated charge to cross it. Because of this, capacitors - like batteries - are limited in their storage capacities.
A natural form of static electrical charge, building of charge, and the crossing of a dielectric's threshold for storage capacity can be seen of clouds and the ground during a thunderstorm. With the air as a dielectric, the clouds acting as one parallel plate, and the ground acting as another, charge is built up in either (typically in the clouds) until the charge of the clouds overwhelms the threshold of the air, and an effect known as a dielectric breakdown occurs. This breakdown results in what we know as lightning.
Much like the clouds, a much smaller household unit could be used to store charge, but it wouldn't be cumulative. This means that unless the storage capacitor was gaining its own charge like a cloud does through particle movement within the clouds, all charge gains will be gathered by one-time exterior suppliers (like the charge from a balloon or gas rod or something else that has gathered a charge). At the time the transfer of energy is complete, that contained charge will be looking for an escape path out of its storage, and leap out unless the next charge was larger than its own, which at the very least would result in a minor electric shock.