Assign Multiple VLANs to a Port – How to Guide

I have a simple question about a network (I am new to this concept so please correct me if I am wrong).

I have a simple network as shown (GNS3):

The network have 3VLANS (VLAN10 = DesignTeam, VLAN30 = EngTeam and VLAN20=Storage). What I would like is for Vlan30 to be accessed by VLAN10 & VLAN30.

I have done some research and I do few things here i.e use router on a stick method but I want to do this via multi-layer switch.

This is what I have done:
First created Vlans
Second assigned port to my VLAN's:
VLAN10 = f1/3
VLAN30 = f1/0
VLAN20 = f1/4
Third
Assign ports to VLAN's:
MainSwitch#conf t
MainSwitch(config)#interface fastEthernet 1/4
MainSwitch(config-if)#switchport access vlan 10
MainSwitch(config-if)#switchport access vlan 30

and then if I run show vlan-switch

I get different output each time (some port gets assigned to wrong VLAN's)

Am I doing anything wrong, anything I shod read further?

EDIT:
if I do: show ip int br i get:

Vlan10                     192.168.10.1    YES manual up                    up      
Vlan20                     192.168.20.1    YES manual up                    up      
Vlan30                     192.168.30.1    YES manual up                    up 

I did show lan-switch and I get:

1    default                          active    Fa1/1, Fa1/2, Fa1/5, Fa1/6
                                            Fa1/7, Fa1/8, Fa1/9, Fa1/10

10   DesignTeam                       active    Fa1/3
20   Storage                          active    Fa1/4
30   EngTeam                          active    Fa1/0

If I access fa1/3 and do switch port access vlan10 then I get:

 1    default                          active    Fa1/1, Fa1/2, Fa1/5, Fa1/6
                                        Fa1/7, Fa1/8, Fa1/9, Fa1/10

10   DesignTeam                       active    Fa1/3 Fa1/4
20   Storage                          active    
30   EngTeam                          active    Fa1/0

As you can see the storage port moved to VLAN10
This is what I want (VLAN 10 & 30 have access to 20):

 1    default                          active    Fa1/1, Fa1/2, Fa1/5, Fa1/6
                                        Fa1/7, Fa1/8, Fa1/9, Fa1/10

10   DesignTeam                       active    Fa1/3 Fa1/4
20   Storage                          active    Fa1/4
30   EngTeam                          active    Fa1/0 Fa1/4

Am I still doing anything wrong?