I am not a native English speaker, so I would like to ask about the usage of 'was + present participle' and past participle without aux in past form. for example, what's the difference between "I was washing clothes" and "I washed clothes" ? which one is the correct form?
Both are correct forms, and often both may be used to refer to the same objective events.
As with aspect generally, the difference is in how the speaker is choosing to refer to the temporal relationships.
In "I was washing clothes", the speaker is focussing on the continuing process of washing the clothes: this is often in order to locate an event temporally within it (eg "When I was washing the clothes, I saw Janet come in"), but it might be for other reasons, such as to emphasise the length of time (eg "I was washing clothes for four hours yesterday").
If the speaker says "I washed clothes", this is referring to the activity as a single event. This does not say anything about whether it took a short or a long time, it just says that for the purposes of the current discourse the speaker is choosing to treat it as a single event.
Idiomatically, "I washed clothes" is not a very common thing to say exactly in that form, but that is for other reasons. "I washed some clothes" or "I washed my clothes" are much more natural. Leaving out the determiner makes it a rather general expression: you might hear it as a habitual activity (eg "I washed clothes every week") but it's a bit unlikely to refer to a single event. On the other hand, "I was washing clothes" is fine: I'm not quite sure where the difference lies.