Gfilui

I want to insert into alias different possible variants of spelling, for example, cat command. Can I do it using some symbol for 'or' or should it be on a new line?

alias at|cart|cst '/bin/cat'

The help for alias indicates that it can assign multiple aliases at once:

alias: alias [-p] [name[=value] ... ]
 Define or display aliases.

 Without arguments, `alias' prints the list of aliases in the reusable
 form `alias NAME=VALUE' on standard output.

 Otherwise, an alias is defined for each NAME whose VALUE is given.
 A trailing space in VALUE causes the next word to be checked for
 alias substitution when the alias is expanded.

So you can use brace expansion to generate the name=value pairs:

alias at,cart,cst='/bin/cat'

So:

$ alias at,cart,cst='/bin/cat'
$ type at cart cst
at is aliased to `/bin/cat'
cart is aliased to `/bin/cat'
cst is aliased to `/bin/cat'

That said, look in to zsh, which has built-in typo correction (which wouldn't help for at, but it would help for the others):

% setopt correct
% sl
zsh: correct `sl' to `ls' [nyae]? y
% setopt correctall
% ls x.v11r4
zsh: correct `x.v11r4' to `X.V11R4' [nyae]? n
/usr/princton/src/x.v11r4 not found
% ls /etc/paswd
zsh: correct to `/etc/paswd' to `/etc/passwd' [nyae]? y
/etc/passwd

If you press y when the shell asks you if you want to correct a
word, it will be corrected. If you press n, it will be left alone.
Pressing a aborts the command, and pressing e brings the line up
for editing again, in case you agree the word is spelled wrong but you
don't like the correction.

I don't think you can assign multiple aliases at once.

But you could loop through a list like this:

for a in cart xat vat xst cst vst dog; do alias "$a"='/bin/cat'; done

Make sure that the aliases are not already in use by other programs (like at in your example).