KEGG offers a REST style API[1] around which you can write scripts to perform large number of automated searches. I haven't read particulars about their API, but official documentation/help should get you going.
The next thing that I could have possibly done is to manually perform GET/POST requests to KEGG website and accordingly parse data from the webpages. This is a bit non trivial but should work.
It depends on how you are meaning orthology. Are you referring to the pathway at all or do you just want to retrieve the orthologs (same gene in different species) for a list of genes? If it is the second, then it is a simple task using the Ensembl REST server.
What information do you want to retrieve specifically?
There reason I asked what data you are looking for specifically is that there is lots of information that is associated with an ortholog. Are you looking for just the ortholog ids? Or the names of the species which have an ortholog? Or the ortholog DNA sequence, or the ortholog protein sequence? In any event, the Ensembl REST server is sufficient to retrieve any/all of this data. You would just need to write a small script, in the programming language of your choice, to iterate through your list of target genes, query the Ensembl REST database, and write the data to a file.