My office server can’t permit me to use Skype and Facebook by any browser. Please let me know how can I use this by any web-based browser?
I'm not real knowledgeable with Skype, but if it's a web-based application that is blocked, using a proxy or VPN should do the trick.
For a proxy I use http://hidemyass.com/
how are Skype and Facebook blocked, can you provide any details?
Have you tried any of these tips, yet:
5 Methods To Bypass Blocked Sites
How to Bypass Firewalls & Get into Blocked Websites in School or at Work with FreeProxy (Windows)
How to Get Past Blocked Sites With PHProxy
6 Tips On How To Unblock A Web Page From Behind A Firewall
How can I access websites blocked at school?
How can I access web sites blocked at work?
How can I access Facebook from school?