Per the ngClass directive documentation, use an object literal with keys of the class names to apply and values of the boolean variables to indicate to add/remove the classes.
It appears that you can use expressions that resolve to booleans in place of a variable in v1.2.6. However, I haven't tested functions.
<li ng-class="{ active: item.name == currentClickState, myAnotherClass: isItemValid(item) }" ng-repeat="item in navigationMenuItems">
<a ui-sref="{{item.name}}" ng-click="selectedItem(item)">{{item.name}}</a>
</li>
P.S. Have a look at Logical Operators. With && the myAnotherClass is only applied if every statements before it is truthy, and active will never be applied as that string is truthy and the next statement is tested. I'm guessing you were intending something like (item.name===currentClickState ? 'active' :'')+(isItemValid(item) ? 'myAnotherClass' :'') (That's a Conditional Operator)