First things first: it’s not wrong to use the past tense form of a な-adjective to modify a noun. This Japanese site on Japanese grammar provides the following examples of how な-adjectives can be used as modifiers:
【Ａ】 新鮮な 野菜を買う。 （連体修飾語）To buy fresh vegetables.
【Ｂ】 新鮮だっ た 野菜が腐る。 （連体修飾語）The formerly fresh vegetables will rot.
【Ｃ】 子どもが 元気に 遊ぶ。 （連用修飾語）
【Ｄ】 子どもは 元気な ほど よい。 （連用修飾語）
Examples A and B clearly show us that both the present tense and past tense forms of な-adjectives are valid modifiers. Also, it is possible to use な-adjective in the past tense in conjunction with a verb in the past tense in order to express a change of state that occurred in the past. For example, we have this article from the Asahi Shimbun:
It contains the following sentence:
Literal translation: There are reasons for which the five rings, beloved in my childhood, became hated.
Idiomatic translation: There are reasons for which I came to hate the five rings I loved in my childhood.
As such, on the surface, I think that all four of your sentences are grammatically possible. (@Leebo, I think your original parsing attempts might also have been correct in that case.) However, the problem here is that we’re looking at a な-adjective and だ・である・です, which doesn’t behave like a typical verb semantically (i.e. in terms of meaning) because all it does is state that something was true or wasn’t true at a particular point. That means that it adds nothing to the information provided by the original な-adjective. As a result, I think sentences #3 and #4 are unnatural, because there’s no reason to phrase things that way: in both sentences #3 and #4, the な-adjective is in the past tense, which tells us that the person ‘was strange’. In that case, what does it matter when he ‘is/was such a person’? For that matter, I think it makes much more sense to think of ‘strange person’ as a single unit, in which case, choosing the ‘simplest’ structure is probably the most natural solution: 変な人でした simply tells us that he was ‘a strange person’ at some point in the past, and that he might not be strange anymore. It contains just as much information as ‘he is a person who was strange in the past’ and ‘he was a person who was strange in the past’ while being much less verbose. Therefore, it makes no sense to use #3 or #4, even if they’re not grammatically wrong.
(If that wasn’t clear, here’s the short version: if you already know the person ‘was weird in the past’, then do you really need to add the words ‘is/was such a person’? Does that provide the reader additional useful information? I think not: if someone ‘was weird’ in 2017, then he ‘was a person who was weird’ in 2018, and ‘is a person who was weird (in 2017)’ right now in 2021. #3 and #4 are grammatically correct, but needlessly complicated because they convey exactly the same information.)
For proof, you can refer to this page in Japanese that contains answers to language questions from… readers of the site, I presume. One reader asks if there’s any context in which「立派だったです」would be acceptable, which I feel is quite similar to your question. The answer given is summed up in its last paragraph:
For now, I treat「美味しいでした。」and「立派だったです。」as no-gos. If you ask why I treat them that way, there is no reason in particular for that, and one can only say that it’s the intuition of a native speaker of Japanese.