Using HTML GET (Arduino is the AP...)

I think this is what you wanted?

#include <ESP8266WiFi.h>
#include <WiFiClient.h> 
#include <ESP8266WebServer.h>
#include <ESP8266HTTPClient.h>

/* Set these to your desired credentials. */
const char *ssid = "ESP8266";
const char *password = "thereisnospoon";

char    inString[32]      ;         // string for incoming serial data
int     stringPos = 0     ;         // string index counter                // what do you use this for?
boolean startRead = false ;         // is reading?

ESP8266WebServer server(80);
WiFiClient client;
/* Go to http://192.168.4.1 in a web browser
 * connected to this access point to see it.
 */

void webpage() {
  server.send(200, "text/html", "<html><body><form  name='frm'  method='post'><input type='text' name='x'   ><input type='submit' value='Submit'>   </form></body></html>");
}
void response(){
  if(server.hasArg("x") && (server.arg("x").length()>0)){ // TODO check that it's not longer than 31 characters
    Serial.print("User entered:\t");
    Serial.println(server.arg("x"));
    inString = server.arg("x");
    server.send(200, "text/html", "<html><body><h1>Successful</h1><a href='/'>Home</a></body></html>");
  } else {
    server.send(400, "text/html", "<html><body><h1>HTTP Error 400</h1><p>Bad request. Please enter a value.</p></body></html>");
  }
}

void setup() {
  Serial.begin(9600);
  Serial.println();
  Serial.println("Configuring access point...");
  Serial.println();
  WiFi.softAP(ssid, password);

  IPAddress myIP = WiFi.softAPIP();
  Serial.println("AP IP address: ");
  Serial.println(myIP);
  server.on("/",HTTP_GET, webpage);
  server.on("/",HTTP_POST,response);
  server.begin();
  Serial.println();
  Serial.println("HTTP server started");
  
}

void loop() {
  server.handleClient();
}

I changed the method to POST, so that you can differentiate between the request of the form page, and the submitting of the form.