I am unable to run any Java applet in all browsers.
Firefox:
Firefox 64 bit does not support the JRE at all.
Firefox 32 still supports the JRE (but support will be withdrawn during 2016). You have to install the 32 bit JRE for this to work.
Mozilla intends to remove support for most NPAPI plugins in Firefox by the end of 2016. Firefox began this process several years ago with manual plugin activation, allowing users to activate plugins only when they were necessary. This decision mirrors actions by other modern browsers, such as Google Chrome and Microsoft Edge, which have already removed support for legacy plugins.
Moreover, since new Firefox platforms do not have to support an existing ecosystem of users and plugins, new platforms such as 64-bit Firefox for Windows will launch without plugin support.
Source NPAPI Plugins in Firefox
Chrome
Chrome no longer supports the JRE.
Java is a NPAPI plugin.
NPAPI plugins are being phased out of Chrome 42. Please note that Chrome will not support NPAPI plugins sometime after April 2015, therefore any websites that use these plugins will all stop working: It will get more difficult to run NPAPI plugins in Chrome.
Source Java Plugins disappear after new Chrome update to Version 42.0.2311.90 m