You really want to correct the waterflow situation first and the only way to do that is to figure out where the water is coming from. If you just try to seal the walls, then you will still have water inside the walls. This water will freeze in winter and cause the walls to crack.

Which wall gets wet and how does that relate to your hill situation? Also are there any leaders at the spots where your walls get wet? Do you have any window wells? Do you have any hardscaping against the wet walls like a driveway or sidewalk? Do you get any seepage through the floor?

As far as cleaning gutters, that can be less important than where the leaders deposit the water. You don't want that to happen against the house. You want the leaders to deposit the water a few feet from the house - at least three or more feet. I've even read recommendations as far as six feet. Since you have sloped land, you may be able to divert the roof runoff with an underground drain that empties past the house. It is hard to say without seeing the site.
The high side of your yard should be graded so the water is diverted out toward the sides of your property. There is probably a way to do it without taking down your deck. Is this where the wall gets wet?

The answer could be as simple as extending your leaders or just building up the soil around the house. Next time it rains heavy, go outside and see how the water puddles against the house or runs toward it if you haven't done so already.

heavy rain turns our backyard into a swamp, and also ends up coming in the basement through window wells, we have sump pumps in wells that work when rain isn't so hard, but we need to redirect water away from house somehow