In a few songs , if I am able to count in both the 4 beats and 3 beats and it still sets perfectly .. how would I know if it is 4/4 or 3/4 ..
Eg1. This is an indian song :
Eg2. Another Indian song :
Determining a piece's time signature isn't only a matter of counting up the beats, it's also about how to notate a piece so it has logical rhythmic units.
Time signature is something that's (1) set by the composer, and (2) for the convenience of musicians who will read and perform the piece. So there are pieces that can be written in more than one way, and I'd like to point out that someone more familiar with Indian music and its conventions could probably give you a more authoritative answer.
"Oh Vennila" sounds to me like it's either in 6/4, pairs of 3/4 measures, or 2/4 in groupings of three measures per phrase. Notating it as 6/4 would be simple in some ways but the measures would get complicated; 2/4 would involve a lot of short measures; and 3/4, while it might seem like a good compromise, is a clunky way to break up phrases. (If you listen to the melody and where the lines break, it's easier to hear this.) Personally, since the rhythm is fairly simple I'd rather have more measures and I'd probably set it up in 2/4, since it works well with the rhythm.
The second video, "Ennavale Adi Ennavale song", sounds more like it's in 3/2 or maybe 6/4, with some sections in 6/8.