In response to the edited question:
Hosts don't generate LSAs; routers do!
If you want to see all the types of LSAs (via show ip ospf database) you could do something like the following:
Type 1 LSA - Router LSA
- Simple - enable the OSPF process and include at least one interface!
router ospf 1
network 0.0.0.0 255.255.255.255 area 0
Type 2 LSA - Network LSA
- Enable OSPF on a network interface that is multiaccess (most easily - ethernet) (note this command is simply an alternate way of enabling OSPF on an interface as compared to the above)
int fa0/0
ip ospf 1 area 0
Type 3 LSA - Summary LSA
You'll need a type 1 LSA to cross an area boundary. Imagine R1 and R2 connected via an ethernet link.
R1:
int l0
ip addr 1.1.1.1 255.255.255.255
ip ospf 1 area 0
int fa0/0
ip addr 10.12.1.1 255.255.255.0
ip ospf 1 area 0
router ospf 1
R2:
int l0
ip addr 2.2.2.2 255.255.255.255
ip ospf 1 area 2
int fa0/0
ip addr 10.12.1.2 255.255.255.0
ip ospf 1 area 0
router ospf 1
Now sho ip ospf database on R1 - and you'll see the LSA for 2.2.2.2/32 as a Type 3 LSA!
I could go on with the rest of the types, not sure if this is helpful or not.