What is the heter for wearing sandals when praying? is it accepted by everone (Rav Ovadia, Rav Eliyahu, Rav Shapira etc.

One should have a respectful attitude towards Tefilah, which should also be reflected by his appearance, therefore if it is disrespectful to wear sandals, one must not wear them for Tefilah, if it is respectful, i.e. you would wear them before an important man - it is permissible. Shulchan Aruch (OC 91, 2)