About ATK Accessibility Tool Kit
SWT has build in accessibility support. For example you can use Orca Screen reader :  to read out loud controls that your mouse hovers over.
Atk is contained in it's own ATK.java file, separate from OS.java. It has it's own atk_custom.h and atk_custom.c where you add custom code.
Much of the core code is located in:
Notion of 'Roles'
SWT widgets are made up of Gtk widgets. Gtk widgets made made of multiple parts (e.g a Table has many Cells). Each widget part can have a role. E.g Table-header role, cell role, Row-header role etc...
A complete list of roles can be found here: 
SWT generally makes use of these roles, but in AccessibleObject it converts Gtk roles to SWT roles that can then be used by people who develop SWT applications and make custom widgets.
ATK has a separate version line from Gtk. In Gtk we have a way to test for the version of Gtk by using GTK_VERSION() macro.
Atk has a similar notion atk_major_version(). .. . However the issue there is that those function and macros were introduced in Atk 2.74. At the time of writing (2015.07.17) SWT supports GTK2.24, which has a minimum spec of Atk 1.3. This means that we can't directly check which version of Atk we are using.
However, if you checkout the gtk git repository and inspect configure.ac, you will observe that it lists the minimum atk version. Based on that you know that given a certain minimum gtk version you can expect a minimum atk version. Thus you can use GTK_VERSION() function in your atk java code.
An example listing at the time of writing:
Gtk2.18 required ATK 1.13.0 Gtk3.0 - Atk 1.3 Gtk3.2 - Atk 2.1.5 Gtk3.4 - Atk 2.2 Gtk3.6 - Atk 2.5.8 Gtk3.8 - Atk 2.7.5 Gtk3.10 - Atk 2.7.5 Gtk3.14 - Atk 2.12.0
When changing ATK, it's recommended to run Orca screen reader to confirm that it's still working well.
In addition, you can use Accerciser ( https://wiki.gnome.org/action/show/Apps/Accerciser?action=show&redirect=Accerciser ) as an inspector tool. It should show the accessibility hierarchy of things.