Datatable vue vuetify POST - PUT AXIOS

Hola. Mi datatable de vuetify con boton de editar y eliminar funciona perfecto en get … pero no puedo hacer post ni put ni delete correctamente a a mi api con axios… me ayudarian con alguna idea o ejemplo. gracias
No entiendo donde poner ni como mi metodo post axios put axios delete axios.

<template v-slot:top>

  <v-toolbar flat color="white">

    <v-toolbar-title>Compania</v-toolbar-title>

    <v-divider

      class="mx-4"

      inset

      vertical

    ></v-divider>

    <v-spacer></v-spacer>

    <v-dialog v-model="dialog" max-width="820px">

      <template v-slot:activator="{ on }">

        <v-btn color="orange" dark class="mb-2" v-on="on">Nueva Compania</v-btn>

      </template>

      <v-card>

        <v-card-title>

          <span class="headline">{{ formTitle }}</span>

        </v-card-title>

        <v-card-text>

    <!-- new company -->

<v-container  id="compania" class="container">

                 <div class="title-container">

                    <div class="orange-bar"></div>



                </div>

  <v-row>

        <v-col  cols="12"   md="12" >

                <v-text-field v-model="editedItem.name" label="Nombre"></v-text-field>      

    </v-col>

                <v-col  cols="12"   md="6" >

                <v-text-field v-model="editedItem.id" label="id"></v-text-field>      

    </v-col>

                <v-col  cols="12"   md="6" >

                <v-text-field v-model="editedItem.status" label="status"></v-text-field>      

    </v-col>

     

  </v-row>

          </v-container>

        </v-card-text>

        <v-card-actions>

          <v-spacer></v-spacer>

          <v-btn color="blue darken-1" text @click="close">Cancel</v-btn>

          <v-btn color="blue darken-1" text @click="save"  @submit.prevent="addCompany">Guardar</v-btn>

        </v-card-actions>

      </v-card>

    </v-dialog>

  </v-toolbar>

</template>

<template v-slot:item.action="{ item }">

  <v-icon

    small

    class="mr-2"

    @click="editItem(item)"

  >

    edit

  </v-icon>

  <v-icon

    small

    @click="deleteItem(item)"

  >

    delete

  </v-icon>

</template>

este es mi script

export default {

data: () => ({

 

    name: 'Compania',

    dialog: false,

         

 headers: [

      {

        text: 'Nombre Compania',

        align: 'left',

        sortable: false,

        value: 'name' },

      { text: 'ID', value: 'id'} ,

     { text: 'Status', value: 'status' },

      { text: 'Actions', value: 'action', sortable: false },

    ],

    

    companies:   [],

    editedIndex: -1,

    editedItem: {

        name: "",

        id:"",

        status:"", 

    },

  defaultItem: {

        name: "",

        id:"",

       status:"", 

      }

}),

computed: {

  formTitle () {

    return this.editedIndex === -1 ? 'Nueva company'  : 'Editar company'

  },

},

watch: {

  dialog (val) {

    val || this.close()

  },

},

created () {

  this.initialize()

},



mounted() {

      this.fetchCompany()

                 },

methods:{

    

  editItem (item) {

    this.editedIndex = this.companies.indexOf(item)

    this.editedItem = Object.assign({}, item)

    this.dialog = true

  },

  deleteItem (item) {

    const index = this.companies.indexOf(item)

    confirm('Seguro desea ELIMINAR el registro?') && this.companies.splice(index, 1)

  },

  close () {

    this.dialog = false

    setTimeout(() => {

      this.editedItem = Object.assign({}, this.defaultItem)

      this.editedIndex = -1

    }, 300)

  },

  save () {

    if (this.editedIndex > -1) {

      

      Object.assign(this.companies[this.editedIndex], this.editedItem)

      

    } else {

      this.companies.push(this.editedItem)

    }

    this.close()

  },

  fetchCompany() {

  //const token = sessionStorage.getItem('token')

  const URL = 'http://192.168.110.105:1337/api/company/get-company'

  this.$axios({

    method: 'get',

    url: URL,

   // headers: {

    //   'Content-Type': 'application/json',

    //   Authorization: `Bearer ${token}`

    // }

  })

    .then(res => {

      this.companies = res.data.data

    })

    .catch(err => {

      // eslint-disable-next-line

      console.log(err)

    })

},