Avocado tree

Hello,

I planted an avocado stone from a store-bought fruit for about 3 years ago. I have cut the upper 1/3 part of the tree about 4 times to push the growth towards the trunk to avoid a tall and skinny tree. Now it's about 80 cm tall, but it only has a few leaves left at the top.
Do anyone have a good suggestion on how I should prune it? I was considering to cut it down to only about 30 cm tall to make the tree strong and healthy, but I'm not sure if that is a good idea.

I had an avocado farm for about a decade in the Dominican Repermies. Avocado varieties are not true to the fruit; so trees grown from seed will produce "criollo" or wild fruit; generally with a relatively round shape and relatively little fruit mass compared to a cultivated variety. Also, the criollo form of an avocado tree is very tall with few low branches surviving - they are predominantly a forest species and saplings won't survive unless they surge to the canopy.

So, what good is a seed-grown avocado? Well, they tend to produce good roots. The common practice is to graft a desirable avocado cultivar onto seed-grown rootstock sooner or later. You'd let the seed grow as it will until it is well-established in soil, and then cut the trunk and graft a branch from a variety that is desired. If you plant the seed and let nature take its course, then you will have a very tall skinny tree and the avocadoes that fall will smash to bits when they hit the ground. Then you can cut that tree down and the stump will produce many new sprouts around the cut; you can graft to some of those and cut away the others - but ever after you have to be on guard against low sprouts from the root that will compete with the grafted branches.

Salat, welcome to permies!

From the photo, my guess is that it isn't getting enough light. It's growing tall to try and find more. Not sure of your home set-up, but I think that would help.

Your tree may do better if it is planted into the garden.  I had my avocado grown from seed outside, and fairly well established before I met a lady who grew them commercially - who said that it won't produce fruit.  I had 2 varieties, and although they flowered and I "helped" with pollination, they never produced.  Lack of water set them back, one died, but the other is still trying to grow back.  
I'm guessing a grafted tree would be the way to go, probably 2 for better results.
A friend had one growing behind the woodshed, and found a fruit on the ground one morning . . he's still not sure whether it grew or if a "helpful" friend had put it there.

Is the avocado tree indoors year round or it goes outside when it's warm?

When people want to make a tree bushier, pinching off the tender tip will promote the buds below to grow into side shoots. However, cutting a big section of stem off is very costly to a young tree. Indoor tree receives less light, thus it has less energy to regrow. It seems except for the 1st or 2nd time, the tree only regrew one shoot after each pruning, possibly on the sunniest side. So it fails to branch out but keeps leaning towards light source over time. The leaves are showing nutrient deficiencies: too few leaves, clustered, light green in color and deformed. The tip is probably stunted too, no top view to see the younger leaves here. If you cut it again, it may die.

If it were my tree, I would give it small amount of complete fertilizer to carry through the winter first. In spring, repot and move outdoors to regain some growth. If the tree puts out lots of leaves and the lower trunk becomes thicker, it will be safe to lower the height.