There are differences of course, but it all depends on the context and how they are being used.
Please keep in mind that they have many different meanings so I am going to give you some examples which are similar but under other circumstances, the meaning might be totally different.
Propose and suggest are quite similar; offer and supply might be similar but the difference is more evident.
Some examples as verbs:
Propose: He proposed an excellent idea.
Suggest: She suggested to do it another way.
Here the meaning is basically similar although "proposed" might be a bit more direct.
Offer: The room offers a nice view.
Provide: The meals were provided for them.
Here again, the meaning is similar and means "to give".
Some examples as a noun:
Proposal: His proposal is yet to be accepted.
Suggestion: My suggestion was to come back home.
Here, the meaning is similar as well; something is being asked, which is basically a proposition.
Offer: She thought about an offer of marriage.
Providing: Without any providing, the tigers would have probably died.
Here the meaning is a proposition for "offer" and a supply for "providing", which means "to give".
That might seem to be confusing, but as I said, it all depends on the context and how you want to use them.
Does that make sense to you?