Sorry for offtopic but its nice that there like minded lithuanians here!

If it's cloudy it's cloudy, there is less sun, and if there is less sun to harvest then photovoltaic panels will produce less. We can maybe optimize the panels for cloudy days but whatever happen they will always produce less energy in cloudy days than sunny days.

So there is multiple alternatives:

• Adapt electric consomption to the weather. I think this is a really important step. With technology we progressively disconnected ourself from the weather. Whatever season it is, whatever the outside temperature we always go to school/work at the same hours, eat the same kind of meals at the same time ... I think with renewables we have to think differently, of we have a sunny day we can do laundry, stay up late, use the electric oven ... In cloudy days we reduce our use of electricity.
• Storage, storage is good for predictable energy variation, maybe to extend a bag day but not more. Whatever amount of storage we install we will still have days when it's not enough, the worst case scenario
• Alternative energy, for when there is no production and the storage is empty then we need to rely on alternative energy. It can be an alternative generator, individual or collective, or it can be having wood stove for cooking and heading and candle for the light. This will cover the x% of hours in the year when we run out.

When I was living on a sailboat, the logic of overcast days was this; that overcast days are often stormy days, so have a wind generator for the "bad weather". But this may not work in your place - sometimes it is just a low-energy day; cloudy and calm.

Of course the other approach is storage; but it tends to be expensive.

A friend has bought vacuum thermal solar heaters: glass tubes with vacuum in it and a black copper thermal conductor that simply heats from the sun's radiation but loses very little energy. He was getting boiling water on an overcast day, I was very surprised to see this passive system going so much over he ambient temperature.

These technologies to capture small amounts of "leftover" energy are neat, but the problem is that by definition you will never get as much out of them as you would from "bulk" energy sources. Often you end up spending more effort/tech/materials for a smaller output, so you're just better off building more solar panels and investing in some storage for cloudy days.

If there happens to be some cheap easy solution to get little pieces of energy here and there, then sure, why not? But it's not going to fill the gap, and it's not worth spending major effort on for a small return.

No. You can install higher efficiency panels which will have a higher yield, but if the radiation from the sun is not there, there is not much to do. On the other hand, you have bifacial solar panels, which are installed vertically and produce energy from both sides. If you have a lot of scattered light through the year, this might be a tech to look for.

This is a somewhat controversial idea, but one possibility would be orbital solar power beamed to the ground as microwave energy.

Since microwaves penetrate cloud cover, photovoltaic panels could operate near their peak efficiency and deliver the energy through the clouds as a beam that can be received even when the clouds are out.

Alternatives would also include nuclear power and long-range transmission from better situated areas.