Exploring all possible models

[chernan6]

Hi,
I am trying to figure if sea lion occupancy in some islands in the Gulf of California can be explained considering local environmental variables.
I recorded a number of variables (that I anticipated a priori to be relevant) at sites both occupied by sea lions and not used (I have data from 54 sites, 30 unused and 24 occupied).
Now I want to generate a set of candidate logistic regression models and use AICc criteria to explore which of these models (and thus environmental variables) explain the occupancy patterns best.
I have reduced my variables to a maximum of 7 in a global model, but that still leaves 127 possible models. My variables are: shade availability, substrate size, abundance of water pools, shoreline shape (angle), slope, substrate coloration, available resting area for sea lions.

My questions are:
1) Should I explore all of 127 models? If so what is the computationally efficient way to do this (I only know how to get AIC values for one model at a time)?
2) If not all should be explored? What could be the criteria for selecting fewer combinations? I feel all variables from those 7 are relevant.

Thanks in advance for your help!