For what my English grammar knowledge is worth¹, that’s some kind of reflexive pronoun, about a non-human object. I’d translate that as “le”, as in :

Je le² pense (bien).

You could also translate it with “ça”, hence :

C’est ce que je pense.

“So” in “so, anyway”, as far as I know, doesn’t have anything to do, and is merely some oral punctuation (is that what you’re tagging “oral” for ?). This could translate³ to “donc”, or “alors”, not bearing much meaning :

Bon, alors… ⁵
Donc, euh…

¹ Not much.
² Actually, if I were to say that, I’d omit the le and say “Je pense bien”, but it’d still be implicit.
³ I have a hard time translating it as I use “anyway”⁴ more and more myself (in “french”).
⁴ En anglais dans le texte.
⁵ Thanks to Evpok.

When a grammar (and not even a dictionnary) has three pages on the use of a word, you may be sure that it hasn’t a simple traduction. To be idiomatic, you’ll need to take the context into account.

For the given examples:

I think so.

Je le pense (aussi), c’est ce que je pense aussi, c’est bien ce que je pense.

So, anyway…

Bon, de toute façon…

Un mot dont l’usage prend trois pages d’explication dans une grammaire, c’est le genre de mot qui n’a pas de traduction hors contexte. Pour les deux exemples donnés :

I think so.

Je le pense (aussi), c’est ce que je pense aussi, c’est bien ce que je pense.

So, anyway…

Bon, de toute façon…

Personnally I link the English ‘so’ with the French ‘ainsi‘, meaning ‘this way’.
I think so is the same as I think this way, in French one could say:

• Je pense ainsi.
• C’est ce que je pense.
• Je le pense.

In ‘So, anyway’ the ‘so’ has a totally different meaning… it’s almost just an interjection… That would be translated to:

• ‘Soit’
• ‘Enfin bref’
• ‘Bon, quoi qu’il en soit’…

Edit: Be careful ‘quoi qu’il en soit‘ only stands for ‘anyway’, and as @LeVieuxGildas has remarked, the ‘soit‘ in ‘quoi qu’il en soit‘ doesn’t correspond to ‘so’, it is really the verb ‘être’ conjugated in this case.

1) I think that the most common equivalent of “I think so” is:

Oui, je pense.

Of course there are many other ways to say that, such as:

En effet. Effectivement. Probablement.

or just: “oui”.

2) For the second sentence, which has a very different meaning. People often says stuff like:

Enfin, bref.

(i.e. okay, I/we have said everything on that topic, let’s conclude or change the topic of conversation)

Voilà.

(i.e. That was what I/we had to say. Let’s speak about something else.)

any many others….