Image Classification using Tensorflow
Since you're doing single label classification, softmax is the best loss function for this, as it maps your final layer logit values to a probability distribution. Sigmoid is used when it's multilabel classification. 
It's always better to use a momentum based optimizer compared to vanilla gradient descent. There's a bunch of such modified optimizers like Adam or RMSProp. Experiment with them to see what works best. Adam is probably going to give you the best performance.
You can add an extra label no_class, so your task will now be a 6+1 label classification. You can feed in some random images with no_class as the label. However the distribution of your random images must match the test image distribution, else it won't generalise.
I am doing transfer-learning/retraining using Tensorflow Inception V3 model. I have 6 labels. A given image can be one single type only, i.e, no multiple class detection is needed. I have three queries:

Which activation function is best for my case? Presently retrain.py file provided by tensorflow uses softmax? What are other methods available? (like sigmoid etc)
Which Optimiser function I should use? (GradientDescent, Adam.. etc)
I want to identify out-of-scope images, i.e. if users inputs a random image, my algorithm should say that it does not belong to the described classes. Presently with 6 classes, it gives one class as a sure output but I do not want that. What are possible solutions for this?

Also, what are the other parameters that we may tweak in tensorflow. My baseline accuracy is 94% and I am looking for something close to 99%.