MQTT bridging with Arduino and ESP8266 - What software should I use?
MQTT is perfectly suited to this application. Here is an overview of a possible configuration. You should be able to find tutorials about each piece of the system. 

On the Raspberry Pi:


Setup a Mosquitto server that can receive messages published by the ESP devices.
Write and run a MQTT client on the RPi that subscribes to the messages published by the ESP devices. This client would then store the data in some sort of permanent data store (database, flat files, whatever).
Write and run on the RPi a web app that reads and presents the data from the data store.


On the ESP devices:


Connect to the same wireless network as the RPi (or set up the RPi as an access point and have the devices connect to it)
Read data from the sensors and publish it to the MQTT server on the RPi.


If you want to push data to the ESP devices -- have them subscribe to certain messages (topics) on the MQTT server and then publish messages in those topics on the server.  Your web app could do this. 

All of this can be done on an isolated network.