HTTP_request and HTTP_response in same irule?

It is absolutely possible, and perhaps desirable, to put all of your events into a single iRule.

when CLIENT_ACCEPTED {
    ...
}
when HTTP_REQUEST {
    ...
}
when HTTP_RESPONSE {
    ...
}
when LB_SELECTED {
    ...
}

It's also worth noting that the order of the events in the iRule is not important.

the plan is to divert traffic to a specific node based on a header value in request, but for calls that don't have a header value, the big ip should round robin the connection and then add a header value to it during response based on the responding node.

Just keep in mind that headers are generally not relayed by the client. In other wordsm if you send a header to a client browser, it will not send it back.

Thanks Kevin. I understand the headers are not going to come back with browser requests - but these are soap calls from a customized solution and I am working with the developers from other side to capture all headers, and preserve a designated one I insert in the subsequent calls. All of this is to mask the fact that an app we run does not share session ids between nodes so round robin breaks calls after login (that have just a valid session id) since they go to a different node. The workaround I proposed is to mark with special header 'tags' which will then be attached to their subsequent calls and I route using the irule to the correct node.

Your solution is fine if the downstream client is programmed to relay the header. You can alternately use a cookie if the client supports it.