If your question was something like, “How do you translate “last week” in Tagalog?”, then those 3 answers/suggestions given to you would be correct. However, they don't mean exactly the same thing. Noong isang linggo – means “a week ago”. We use this phrase rather loosely in the sense that it may refer to from 1 to a couple of weeks prior to the present week. So, think of it more like “a week or so ago”. “Umulan noong isang linggo” = It rained last week (or a week ago, more or less). Noong nakaraang linggo – means “the week that just passed”. This would be the more “accurate” reference to the previous week as its relation to the present week is implied - “nakaraan” (to have passed). “Umulan noong nakaraang linggo” = It rained last week (or on one of the days of the week that just passed). Noong pinakahuling linggo (ng) – means “on the very last week (of)”. This indicates the last week of any time period in the past that may contain the week being referred to. “Pinaka” means “the most” and “huli” means “the last”. “Pinaka” may be omitted, unless you want to give emphasis to that week being the last one of that period in time. “Umulan noong (pinaka)huling linggo ng Julyo” = It rained on the (very) last week of July”; “Umulan noong (pinaka)huling linggo ng 2007. = It rained on the (very) last week of 2007. BTW, “noong” is an indicator of a time in the past. “Sa” would be its counterpart, referring to the future. Hence, “sa isang linggo” would mean “next week” and “sa pinakahuling linggo” would refer to a particular week in the future, e.g., “sa (pinaka)huling linggo nitong taon” = the (very) last week of this year. For “nakaraan”, it becomes “susunod” (to follow) - “sa susunod na linggo” = the week that will follow = next week.

I don't know if they all have the same meaning exactly, I would guess that 'Noong Isang Linggo' means like 'before, a week ago...,' - I think you would use it to place the following statement which follows in the past, one week ako. Like 'noong isang linggo, pumunta ako sa Maynila'. PinakahulinG linggo - the very last week. Maybe it is important in the context to be precise? I don't think you could start a sentence with this, as opposed to the other two examples. Nakaraang Linggo - last (the previous) week. Seems similar to the first one, to me. Anyway, I am sure you will receive a more comprehensive answer soon, I am interested in the response also :)