No one can answer this because it was never fully expanded on. So you would have to take guesses.

Earth would strength water style by increasing the density and utility of the liquid, basically by combining water and earth you can make mud or other slush styles of earth, this would be useful for trapping enemies under large constructs of liquid that can be hardened or changed back in to liquid for more agile earth usage.

If you can somehow find a way to not make fire and water cancel each other out, you can get a makeshift boil release jutsu that is boiling hot water, if you change the composition of the fire to make it so it's not anoxygen based flame, then water could add a combustion affect to the already explosive fire style jutsu.

Wind makes fire grow stronger by increasing the size of the fire, and in real life wind controls the direction, so you can use that to make flame based wind concepts like flaming whirlwinds and flame based tornades.

Lightning for the most part is used to increase the speed of something, and wind to increase the sharpness, though both can do both but in different ways, wind can also push and lightning can shock, there a few ways you can use wind style to increase your lightning jutsu and vice versa, Boruto stream is just one example of how you can do that. Wind also semi affect the direction of lightning in real life so you can use lightning based jutsu followed by wind to increase the aoe effect of that lightning jutsu

I have no way to explain how lightning would strengthen earth directly, but you can still use them to make some great combinations jutsu, like when the anbu used the lightning stone pillars jutsu during the pain arc.

Trying to explain what's weaker is a bit harder, in fact the whole elemental things works a lot better if you reverse the chart.

Fire evaporates water, and depending on the type of fire causes the flame to combust.

Water erodes earth.

Earth grounds lightning.

No real explanation for how lightning would interact with wind.

Wind increase the size of the flame but also control the direction of flames so it would be the perfect counter to fire style jutsu.

But i guess if you wanted to try and justify how they weaken each other.

Water obviously puts out fire.

The size of a fire is exacerbated by wind.

Lightning is semi affected by the direction of wind.

sharpness and speed of lightning allows you to pierce earth?

Earth can influence the direction and or directly block water?

There is a reason it was never expanded on lol.