I have two villagers right now who are taking care of twins.

Basically, when you put the villagers on each other to "go indoors", you don't really have to let them go indoors...you see right away if they have a baby or not, since the number changes where it states the number of population. So I just grabbed the villagers and put them on each other again, and the number changes again sometimes... resulting in twins. I copied the screen shot for my villagers... here it is, with two pairs of twins.

Twins ... Triplets.... yup
Depending on your level of Fertility multiple births happen

ah cool!

No multiple births in my village. Is there any way for it to happen with only Level 1 Fertility?

nope unless you get some babys in crate!

I have level one fertility and I just got twins - though this is rare and a random occurrence - but obviously possible.

Ok, just wondering.

Yep ive had a few lots of twins and triplets

I had lots of twins and triplets when I did something that I can't tell you about (cause it would spoil it). I left my villagers at a population of 35 to go out for a short while and, to my surprise and dismay, when I came back I had reached the limit of 90 villagers! A lot of twins and triplets in the bunch.

Is there a certain level of fertility needed in order to create twins and triplets?

You usually wont see twins unless you have Level 2, rarely will twins be born without it, but it happens. Triplets tho, I havent seen any born in any of my villages without Level 3. Can't say for anyone else.