Each of the words and expressions have more than one meaning.  I will try to explain only those meanings which are relatively common to all the words and expressions.

"escape" means to avoid being confined or restrained ("He robbed the bank, and managed to escape capture") or to free oneself of confinement or restraint after having been confined or restrained. ("He was captured by the police, but escaped from jail the next day.)  

"elude" means to avoid being confined or restrained, and usually connotes cunning or daring.  "The daring and shrewed has criminal eluded the police for many years."  (He was never caught.)   "elude" would not be used after a person is captured.  For example, you could say, "He escaped from jail," but you would not say "He eluded from jail."

"slip off" means to take something off by sliding them off one's body.   "I don't know how he did it, but somehow he was able to slip off his handcuffs."  "slip off" can also mean to leave quickly and quietly.  "The mother wanted her children to do their homework, but when she wasn't looking they slipped off to the movie theater."

"get rid of" means to dispose of someone or something.   It is not the speaker who leaves, escapes, or eludes.  Instead, the speaker frees himself from someone or something else.    "I finished drinking my beer.  Where can I get rid of the bottle?"   Teenage boy:  "I wish I could get rid of my little brother when my girlfriend comes to visit me."   

What are differences, part 1

Could you explain the differences in usage: get rid of / elude / slip off / escape.

In Russian "убегать", "ускользать" применимо и к людям, и к предметам, и к мыслям.
could describe men, things, thoughts.

get rid of  - to dispose of something, or discard something.

"I will get rid of these clothes" means "I will dispose of these clothes" (as in throw them in the bin or something similar).

elude  - to avoid or escape by speed, cleverness, or trickery etc

"The criminal was able to elude capture by the police" means "The criminal was able to avoid capture by the police" 

slip off - can mean to remove something like an article of clothing, or to slide off a surface.

'I will just slip off this shirt' means "I will just take off (or remove) this shirt.

"Careful or you might slip off that rock" means "Be careful or you might slide of that rock" (Using "slip" in this instance implies that the rock is slippery. 

escape - to get away from or avoid capture.

"The prisoner was able to escape from police custody" means "The prisoner was able to get away from police custody"

You could use variations 3 of the above in similar ways for some situations. For example-

"The criminal was able to elude capture by the police"  

"The criminal was able to slip away from the police"

"The criminal was able to escape from the police"

all have basically the same meaning.

I hope that helps

What is difference, part 1

Could you explain the difference in usage: get rid of / elude / slip off / escape.

In Russian "убегать", "ускользать" применимо и к людям, и к предметам, и к мыслям.
could describe men, things, thoughts.

What is difference, part 1

Could you explain the difference in usage: get rid of / elude / slip off / escape.

In Russian "убегать", "ускользать" применимо и к людям, и к предметам, и к мыслям.
could describe men, things, thoughts.