Shall I inquire about the status of my application?
We don't know the schedule of skype interviews for this particular institution, or the review process that happens after skype interviews and before candidates are invited to campus.  In my recent experience of chairing search committees, the top candidates got invitations for on-campus interviews within a week of the end of the skype interviews (which typically took us about a week to do.)  It's obviously in our interest to do this as quickly as possible.  However, this process could be delayed by administrative indecision (e.g. if the administration is uncertain about whether or not they'll have enough of a budget to actually hire someone.)

It's quite possible that the search committee has sent out invitations for on-campus interviews.  If you contacted the search committee chair he/she would probably tell you whether or not this has happened.    

Even if the initial round of invitations have gone out and you haven't gotten one, don't give up hope yet.  It's possible that some other candidate will decline the chance to interview on campus and you'll get an interview later.  In the past I've had to say to candidates something like "We sent out invitations for on-campus interviews to three candidates earlier this week, and we're still waiting for responses from two of them.  We may be sending out additional invitations."  This doesn't tell the candidate anything specific about whether they might be next on the list or much further down (or even off the list entirely due to a bad phone interview.)  

I can't think of any reason not to politely ask the search committee chair about the status of the search.  You could also start checking the institution's calendar for seminars to see if anyone that looks like a faculty candidate (or is explicitly named as such) might be scheduled.