They are similar phrases, except for "look after" which only resembles the others :)
Peachey gave a good description of the sentence structure differences. I think there are some slight meaning differences as well.
X is similar to Y: Means X and Y are close to the same.
X and Y are alike: There is some similarity. This feels a little more formal than "similar".
X resembles Y: X seems, on the surface, similar to Y, often visually. It might or might not actually be similar. It's a slightly more formal word, although there is one common phrase "family resemblance", which means the way two relatives look similar.
X looks like Y: Like "resembles", but less formal.