I have a raster layer with pixel values of 1 and 0. I would like to extract values from several other, overlaying, raster layers for all the cells that equal 1.
Is there any ArcMap tool similar to extract multi values to point that I could use?
The tool you want is called the Sample Tool. It requires the Spatial Analyst extension. The input location can be a raster or point features. I've never tried it with a raster, but it should work with what you have. However, you will need to convert your zero values to Null first using the SetNull tool.
From the documentation:
When the input location is a raster, the set of location cells consists of all cells that have a value of zero or greater. Cells that have NoData values are not included in the location set. A location raster can be easily created using the extraction tools.
When the location input is raster, for best results, the cell size and registration of the input rasters and the location raster should be the same.
You can input your other rasters and the output will be a table with attributes from values at all your 1 values.
More about how the Sample Tool works here.