Help me distinguish between generally, usually, basically and normally?

Well, it depends on the connotation you’re going for. That is:

Normally/Generally: These imply that there may be some rational reason (a non-general or non-normal case) for someone to be doing this. It also seems to suggest that the person you’re talking to is either walking around naked in public, or is considering it.

Basically: This implies that people almost never do this, and it’s a basic or fundamental social rule that you don’t do this. “In the most essential respects; fundamentally: “a basically simple idea”.”

Usually: Sort of up there with Normally/Generally, but I think it implies a less-strong bonding than Normally or Generally. I think implies more habitual than a social rule.

I would go with Normally or Usually in the case you describe. Generally means in general. Basically, means at base.

“Basically” is now overused as a means of jumpstarting a sentence.

Basically, I don’t know what I am going to say and want to buy some time.

“Normally” implies that there is a norm related to your response. If in a nudist colony, you can say, “Normally, people do walk around naked in public.”

I see “usually” and “generally” as interchangeable.

The first week in June is a good time to plan an outdoor wedding because ”Usually it doesn’t rain. In general, this generalization works.”

Are you going to tell us which certain situation you want to use one of these words in?

There is a certain amount of nuance, in terms of meaning and usage with these words, but
I agree with @gailcalled. “Basically” is word you really shouldn’t, generally, have to use; it is overused and is basically meaningless at this point. :-) And overusing that word is a sin I am sometimes guilty of.

“Usually” and “generally” are pretty much interchangeable.

For me, with “normally” and “generally,” normally is slightly more specific than generally, I think. For example, if I were working somewhere and someone asked me to make an exception in their case, regarding a matter of policy, I would probably say “Normally, we don’t make exceptions in cases like this, but…” rather than “Generally, we don’t make exceptions in cases like this ...”

It’s kind of a stylistic call rather than a matter of grammar, etc, I think.

Basically, as a general personal rule, I would usually avoid normally.
Normally, at a most basic personal level, I would usually prefer to use generally.
Generally, I find that, basically, I don’t personally normally like to say usually.
Usually, if not normally, but most definitely generally, I personally try to never use basically.